d Bessel function of the second kind of real order                         `v`
   kve               -- Exponentially scaled modified Bessel function of the                         second kind.
   iv                -- Modified Bessel function of the first kind of real order.
   ive               -- Exponentially scaled modified Bessel function of the                         first kind.
   hankel1           -- Hankel function of the first kind.
   hankel1e          -- Exponentially scaled Hankel function of the first kind.
   hankel2           -- Hankel function of the second kind.
   hankel2e          -- Exponentially scaled Hankel function of the second kind.
   wright_bessel     -- Wright's generalized Bessel function.
   log_wright_bessel -- Logarithm of Wright's generalized Bessel function.

The following function does not accept NumPy arrays (it is not a
universal function):

.. autosummary::
   :toctree: generated/

   lmbda -- Jahnke-Emden Lambda function, Lambdav(x).

Zeros of Bessel functions
^^^^^^^^^^^^^^^^^^^^^^^^^

The following functions do not accept NumPy arrays (they are not
universal functions):

.. autosummary::
   :toctree: generated/

   jnjnp_zeros -- Compute zeros of integer-order Bessel functions Jn and Jn'.
   jnyn_zeros  -- Compute nt zeros of Bessel functions Jn(x), Jn'(x), Yn(x), and Yn'(x).
   jn_zeros    -- Compute zeros of integer-order Bessel function Jn(x).
   jnp_zeros   -- Compute zeros of integer-order Bessel function derivative Jn'(x).
   yn_zeros    -- Compute zeros of integer-order Bessel function Yn(x).
   ynp_zeros   -- Compute zeros of integer-order Bessel function derivative Yn'(x).
   y0_zeros    -- Compute nt zeros of Bessel function Y0(z), and derivative at each zero.
   y1_zeros    -- Compute nt zeros of Bessel function Y1(z), and derivative at each zero.
   y1p_zeros   -- Compute nt zeros of Bessel derivative Y1'(z), and value at each zero.

Faster versions of common Bessel functions
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

.. autosummary::
   :toctree: generated/

   j0  -- Bessel function of the first kind of order 0.
   j1  -- Bessel function of the first kind of order 1.
   y0  -- Bessel function of the second kind of order 0.
   y1  -- Bessel function of the second kind of order 1.
   i0  -- Modified Bessel function of order 0.
   i0e -- Exponentially scaled modified Bessel function of order 0.
   i1  -- Modified Bessel function of order 1.
   i1e -- Exponentially scaled modified Bessel function of order 1.
   k0  -- Modified Bessel function of the second kind of order 0, :math:`K_0`.
   k0e -- Exponentially scaled modified Bessel function K of order 0
   k1  -- Modified Bessel function of the second kind of order 1, :math:`K_1(x)`.
   k1e -- Exponentially scaled modified Bessel function K of order 1.

Integrals of Bessel functions
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

.. autosummary::
   :toctree: generated/

   itj0y0     -- Integrals of Bessel functions of order 0.
   it2j0y0    -- Integrals related to Bessel functions of order 0.
   iti0k0     -- Integrals of modified Bessel functions of order 0.
   it2i0k0    -- Integrals related to modified Bessel functions of order 0.
   besselpoly -- Weighted integral of a Bessel function.

Derivatives of Bessel functions
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

.. autosummary::
   :toctree: generated/

   jvp  -- Compute nth derivative of Bessel function Jv(z) with respect to `z`.
   yvp  -- Compute nth derivative of Bessel function Yv(z) with respect to `z`.
   kvp  -- Compute nth derivative of real-order modified Bessel function Kv(z)
   ivp  -- Compute nth derivative of modified Bessel function Iv(z) with respect to `z`.
   h1vp -- Compute nth derivative of Hankel function H1v(z) with respect to `z`.
   h2vp -- Compute nth derivative of Hankel function H2v(z) with respect to `z`.

Spherical Bessel functions
^^^^^^^^^^^^^^^^^^^^^^^^^^

.. autosummary::
   :toctree: generated/

   spherical_jn -- Spherical Bessel function of the first kind or its derivative.
   spherical_yn -- Spherical Bessel function of the second kind or its derivative.
   spherical_in -- Modified spherical Bessel function of the first kind or its derivative.
   spherical_kn -- Modified spherical Bessel function of the second kind or its derivative.

Riccati-Bessel functions
^^^^^^^^^^^^^^^^^^^^^^^^

The following functions do not accept NumPy arrays (they are not
universal functions):

.. autosummary::
   :toctree: generated/

   riccati_jn -- Compute Ricatti-Bessel function of the first kind and its derivative.
   riccati_yn -- Compute Ricatti-Bessel function of the second kind and its derivative.

Struve functions
----------------

.. autosummary::
   :toctree: generated/

   struve       -- Struve function.
   modstruve    -- Modified Struve function.
   itstruve0    -- Integral of the Struve function of order 0.
   it2struve0   -- Integral related to the Struve function of order 0.
   itmodstruve0 -- Integral of the modified Struve function of order 0.


Raw statistical functions
-------------------------

.. seealso:: :mod:`scipy.stats`: Friendly versions of these functions.

Binomial distribution
^^^^^^^^^^^^^^^^^^^^^

.. autosummary::
   :toctree: generated/

   bdtr         -- Binomial distribution cumulative distribution function.
   bdtrc        -- Binomial distribution survival function.
   bdtri        -- Inverse function to `bdtr` with respect to `p`.
   bdtrik       -- Inverse function to `bdtr` with respect to `k`.
   bdtrin       -- Inverse function to `bdtr` with respect to `n`.

Beta distribution
^^^^^^^^^^^^^^^^^

.. autosummary::
   :toctree: generated/

   btdtria      -- Inverse of `betainc` with respect to `a`.
   btdtrib      -- Inverse of `betainc` with respect to `b`.

F distribution
^^^^^^^^^^^^^^

.. autosummary::
   :toctree: generated/

   fdtr         -- F cumulative distribution function.
   fdtrc        -- F survival function.
   fdtri        -- The `p`-th quantile of the F-distribution.
   fdtridfd     -- Inverse to `fdtr` vs dfd.

Gamma distribution
^^^^^^^^^^^^^^^^^^

.. autosummary::
   :toctree: generated/

   gdtr         -- Gamma distribution cumulative distribution function.
   gdtrc        -- Gamma distribution survival function.
   gdtria       -- Inverse of `gdtr` vs a.
   gdtrib       -- Inverse of `gdtr` vs b.
   gdtrix       -- Inverse of `gdtr` vs x.

Negative binomial distribution
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

.. autosummary::
   :toctree: generated/

   nbdtr        -- Negative binomial cumulative distribution function.
   nbdtrc       -- Negative binomial survival function.
   nbdtri       -- Inverse of `nbdtr` vs `p`.
   nbdtrik      -- Inverse of `nbdtr` vs `k`.
   nbdtrin      -- Inverse of `nbdtr` vs `n`.

Noncentral F distribution
^^^^^^^^^^^^^^^^^^^^^^^^^

.. autosummary::
   :toctree: generated/

   ncfdtr       -- Cumulative distribution function of the non-central F distribution.
   ncfdtridfd   -- Calculate degrees of freedom (denominator) for the noncentral F-distribution.
   ncfdtridfn   -- Calculate degrees of freedom (numerator) for the noncentral F-distribution.
   ncfdtri      -- Inverse cumulative distribution function of the non-central F distribution.
   ncfdtrinc    -- Calculate non-centrality parameter for non-central F distribution.

Noncentral t distribution
^^^^^^^^^^^^^^^^^^^^^^^^^

.. autosummary::
   :toctree: generated/

   nctdtr       -- Cumulative distribution function of the non-central `t` distribution.
   nctdtridf    -- Calculate degrees of freedom for non-central t distribution.
   nctdtrit     -- Inverse cumulative distribution function of the non-central t distribution.
   nctdtrinc    -- Calculate non-centrality parameter for non-central t distribution.

Normal distribution
^^^^^^^^^^^^^^^^^^^

.. autosummary::
   :toctree: generated/

   nrdtrimn     -- Calculate mean of normal distribution given other params.
   nrdtrisd     -- Calculate standard deviation of normal distribution given other params.
   ndtr         -- Normal cumulative distribution function.
   log_ndtr     -- Logarithm of normal cumulative distribution function.
   ndtri        -- Inverse of `ndtr` vs x.
   ndtri_exp    -- Inverse of `log_ndtr` vs x.

Poisson distribution
^^^^^^^^^^^^^^^^^^^^

.. autosummary::
   :toctree: generated/

   pdtr         -- Poisson cumulative distribution function.
   pdtrc        -- Poisson survival function.
   pdtri        -- Inverse to `pdtr` vs m.
   pdtrik       -- Inverse to `pdtr` vs k.

Student t distribution
^^^^^^^^^^^^^^^^^^^^^^

.. autosummary::
   :toctree: generated/

   stdtr        -- Student t distribution cumulative distribution function.
   stdtridf     -- Inverse of `stdtr` vs df.
   stdtrit      -- Inverse of `stdtr` vs `t`.

Chi square distribution
^^^^^^^^^^^^^^^^^^^^^^^

.. autosummary::
   :toctree: generated/

   chdtr        -- Chi square cumulative distribution function.
   chdtrc       -- Chi square survival function.
   chdtri       -- Inverse to `chdtrc`.
   chdtriv      -- Inverse to `chdtr` vs `v`.

Non-central chi square distribution
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

.. autosummary::
   :toctree: generated/

   chndtr       -- Non-central chi square cumulative distribution function.
   chndtridf    -- Inverse to `chndtr` vs `df`.
   chndtrinc    -- Inverse to `chndtr` vs `nc`.
   chndtrix     -- Inverse to `chndtr` vs `x`.

Kolmogorov distribution
^^^^^^^^^^^^^^^^^^^^^^^

.. autosummary::
   :toctree: generated/

   smirnov      -- Kolmogorov-Smirnov complementary cumulative distribution function.
   smirnovi     -- Inverse to `smirnov`.
   kolmogorov   -- Complementary cumulative distribution function of Kolmogorov distribution.
   kolmogi      -- Inverse function to `kolmogorov`.

Box-Cox transformation
^^^^^^^^^^^^^^^^^^^^^^

.. autosummary::
   :toctree: generated/

   boxcox       -- Compute the Box-Cox transformation.
   boxcox1p     -- Compute the Box-Cox transformation of 1 + `x`.
   inv_boxcox   -- Compute the inverse of the Box-Cox transformation.
   inv_boxcox1p -- Compute the inverse of the Box-Cox transformation.


Sigmoidal functions
^^^^^^^^^^^^^^^^^^^

.. autosummary::
   :toctree: generated/

   logit        -- Logit ufunc for ndarrays.
   expit        -- Logistic sigmoid function.
   log_expit    -- Logarithm of the logistic sigmoid function.

Miscellaneous
^^^^^^^^^^^^^

.. autosummary::
   :toctree: generated/

   tklmbda      -- Tukey-Lambda cumulative distribution function.
   owens_t      -- Owen's T Function.


Information Theory functions
----------------------------

.. autosummary::
   :toctree: generated/

   entr         -- Elementwise function for computing entropy.
   rel_entr     -- Elementwise function for computing relative entropy.
   kl_div       -- Elementwise function for computing Kullback-Leibler divergence.
   huber        -- Huber loss function.
   pseudo_huber -- Pseudo-Huber loss function.


Gamma and related functions
---------------------------

.. autosummary::
   :toctree: generated/

   gamma        -- Gamma function.
   gammaln      -- Logarithm of the absolute value of the Gamma function for real inputs.
   loggamma     -- Principal branch of the logarithm of the Gamma function.
   gammasgn     -- Sign of the gamma function.
   gammainc     -- Regularized lower incomplete gamma function.
   gammaincinv  -- Inverse to `gammainc`.
   gammaincc    -- Regularized upper incomplete gamma function.
   gammainccinv -- Inverse to `gammaincc`.
   beta         -- Beta function.
   betaln       -- Natural logarithm of absolute value of beta function.
   betainc      -- Incomplete beta integral.
   betaincc     -- Complemented incomplete beta integral.
   betaincinv   -- Inverse function to beta integral.
   betainccinv  -- Inverse of the complemented incomplete beta integral.
   psi          -- The digamma function.
   rgamma       -- Gamma function inverted.
   polygamma    -- Polygamma function n.
   multigammaln -- Returns the log of multivariate gamma, also sometimes called the generalized gamma.
   digamma      -- psi(x[, out]).
   poch         -- Rising factorial (z)_m.

Error function and Fresnel integrals
------------------------------------

.. autosummary::
   :toctree: generated/

   erf           -- Returns the error function of complex argument.
   erfc          -- Complementary error function, ``1 - erf(x)``.
   erfcx         -- Scaled complementary error function, ``exp(x**2) * erfc(x)``.
   erfi          -- Imaginary error function, ``-i erf(i z)``.
   erfinv        -- Inverse function for erf.
   erfcinv       -- Inverse function for erfc.
   wofz          -- Faddeeva function.
   dawsn         -- Dawson's integral.
   fresnel       -- Fresnel sin and cos integrals.
   fresnel_zeros -- Compute nt complex zeros of sine and cosine Fresnel integrals S(z) and C(z).
   modfresnelp   -- Modified Fresnel positive integrals.
   modfresnelm   -- Modified Fresnel negative integrals.
   voigt_profile -- Voigt profile.

The following functions do not accept NumPy arrays (they are not
universal functions):

.. autosummary::
   :toctree: generated/

   erf_zeros      -- Compute nt complex zeros of error function erf(z).
   fresnelc_zeros -- Compute nt complex zeros of cosine Fresnel integral C(z).
   fresnels_zeros -- Compute nt complex zeros of sine Fresnel integral S(z).

Legendre functions
------------------

.. autosummary::
   :toctree: generated/

   legendre_p                 -- Legendre polynomials of the first kind.
   legendre_p_all             -- All Legendre polynomials of the first kind up to a specified order.
   assoc_legendre_p           -- Associated Legendre polynomials of the first kind.
   assoc_legendre_p_all       -- All associated Legendre polynomials of the first kind up to a specified order and degree.
   sph_legendre_p             -- Spherical Legendre polynomials of the first kind.
   sph_legendre_p_all         -- All spherical Legendre polynomials of the first kind up to a specified order and degree.
   sph_harm_y                 -- Spherical harmonics.
   sph_harm_y_all             -- All spherical harmonics up to a specified order and degree.

The following functions are in the process of being deprecated in favor of the above,
which provide a more flexible and consistent interface.

.. autosummary::
   :toctree: generated/

   lpmv                       -- Associated Legendre function of integer order and real degree.
   sph_harm                   -- Compute spherical harmonics.
   clpmn                      -- Associated Legendre function of the first kind for complex arguments.
   lpn                        -- Legendre function of the first kind.
   lqn                        -- Legendre function of the second kind.
   lpmn                       -- Sequence of associated Legendre functions of the first kind.
   lqmn                       -- Sequence of associated Legendre functions of the second kind.

Ellipsoidal harmonics
---------------------

.. autosummary::
   :toctree: generated/

   ellip_harm   -- Ellipsoidal harmonic functions E^p_n(l).
   ellip_harm_2 -- Ellipsoidal harmonic functions F^p_n(l).
   ellip_normal -- Ellipsoidal harmonic normalization constants gamma^p_n.

Orthogonal polynomials
----------------------

The following functions evaluate values of orthogonal polynomials:

.. autosummary::
   :toctree: generated/

   assoc_laguerre   -- Compute the generalized (associated) Laguerre polynomial of degree n and order k.
   eval_legendre    -- Evaluate Legendre polynomial at a point.
   eval_chebyt      -- Evaluate Chebyshev polynomial of the first kind at a point.
   eval_chebyu      -- Evaluate Chebyshev polynomial of the second kind at a point.
   eval_chebyc      -- Evaluate Chebyshev polynomial of the first kind on [-2, 2] at a point.
   eval_chebys      -- Evaluate Chebyshev polynomial of the second kind on [-2, 2] at a point.
   eval_jacobi      -- Evaluate Jacobi polynomial at a point.
   eval_laguerre    -- Evaluate Laguerre polynomial at a point.
   eval_genlaguerre -- Evaluate generalized Laguerre polynomial at a point.
   eval_hermite     -- Evaluate physicist's Hermite polynomial at a point.
   eval_hermitenorm -- Evaluate probabilist's (normalized) Hermite polynomial at a point.
   eval_gegenbauer  -- Evaluate Gegenbauer polynomial at a point.
   eval_sh_legendre -- Evaluate shifted Legendre polynomial at a point.
   eval_sh_chebyt   -- Evaluate shifted Chebyshev polynomial of the first kind at a point.
   eval_sh_chebyu   -- Evaluate shifted Chebyshev polynomial of the second kind at a point.
   eval_sh_jacobi   -- Evaluate shifted Jacobi polynomial at a point.

The following functions compute roots and quadrature weights for
orthogonal polynomials:

.. autosummary::
   :toctree: generated/

   roots_legendre    -- Gauss-Legendre quadrature.
   roots_chebyt      -- Gauss-Chebyshev (first kind) quadrature.
   roots_chebyu      -- Gauss-Chebyshev (second kind) quadrature.
   roots_chebyc      -- Gauss-Chebyshev (first kind) quadrature.
   roots_chebys      -- Gauss-Chebyshev (second kind) quadrature.
   roots_jacobi      -- Gauss-Jacobi quadrature.
   roots_laguerre    -- Gauss-Laguerre quadrature.
   roots_genlaguerre -- Gauss-generalized Laguerre quadrature.
   roots_hermite     -- Gauss-Hermite (physicist's) quadrature.
   roots_hermitenorm -- Gauss-Hermite (statistician's) quadrature.
   roots_gegenbauer  -- Gauss-Gegenbauer quadrature.
   roots_sh_legendre -- Gauss-Legendre (shifted) quadrature.
   roots_sh_chebyt   -- Gauss-Chebyshev (first kind, shifted) quadrature.
   roots_sh_chebyu   -- Gauss-Chebyshev (second kind, shifted) quadrature.
   roots_sh_jacobi   -- Gauss-Jacobi (shifted) quadrature.

The functions below, in turn, return the polynomial coefficients in
``orthopoly1d`` objects, which function similarly as `numpy.poly1d`.
The ``orthopoly1d`` class also has an attribute ``weights``, which returns
the roots, weights, and total weights for the appropriate form of Gaussian
quadrature. These are returned in an ``n x 3`` array with roots in the first
column, weights in the second column, and total weights in the final column.
Note that ``orthopoly1d`` objects are converted to `~numpy.poly1d` when doing
arithmetic, and lose information of the original orthogonal polynomial.

.. autosummary::
   :toctree: generated/

   legendre    -- Legendre polynomial.
   chebyt      -- Chebyshev polynomial of the first kind.
   chebyu      -- Chebyshev polynomial of the second kind.
   chebyc      -- Chebyshev polynomial of the first kind on :math:`[-2, 2]`.
   chebys      -- Chebyshev polynomial of the second kind on :math:`[-2, 2]`.
   jacobi      -- Jacobi polynomial.
   laguerre    -- Laguerre polynomial.
   genlaguerre -- Generalized (associated) Laguerre polynomial.
   hermite     -- Physicist's Hermite polynomial.
   hermitenorm -- Normalized (probabilist's) Hermite polynomial.
   gegenbauer  -- Gegenbauer (ultraspherical) polynomial.
   sh_legendre -- Shifted Legendre polynomial.
   sh_chebyt   -- Shifted Chebyshev polynomial of the first kind.
   sh_chebyu   -- Shifted Chebyshev polynomial of the second kind.
   sh_jacobi   -- Shifted Jacobi polynomial.

.. warning::

   Computing values of high-order polynomials (around ``order > 20``) using
   polynomial coefficients is numerically unstable. To evaluate polynomial
   values, the ``eval_*`` functions should be used instead.


Hypergeometric functions
------------------------

.. autosummary::
   :toctree: generated/

   hyp2f1 -- Gauss hypergeometric function 2F1(a, b; c; z).
   hyp1f1 -- Confluent hypergeometric function 1F1(a, b; x).
   hyperu -- Confluent hypergeometric function U(a, b, x) of the second kind.
   hyp0f1 -- Confluent hypergeometric limit function 0F1.


Parabolic cylinder functions
----------------------------

.. autosummary::
   :toctree: generated/

   pbdv -- Parabolic cylinder function D.
   pbvv -- Parabolic cylinder function V.
   pbwa -- Parabolic cylinder function W.

The following functions do not accept NumPy arrays (they are not
universal functions):

.. autosummary::
   :toctree: generated/

   pbdv_seq -- Parabolic cylinder functions Dv(x) and derivatives.
   pbvv_seq -- Parabolic cylinder functions Vv(x) and derivatives.
   pbdn_seq -- Parabolic cylinder functions Dn(z) and derivatives.

Mathieu and related functions
-----------------------------

.. autosummary::
   :toctree: generated/

   mathieu_a -- Characteristic value of even Mathieu functions.
   mathieu_b -- Characteristic value of odd Mathieu functions.

The following functions do not accept NumPy arrays (they are not
universal functions):

.. autosummary::
   :toctree: generated/

   mathieu_even_coef -- Fourier coefficients for even Mathieu and modified Mathieu functions.
   mathieu_odd_coef  -- Fourier coefficients for even Mathieu and modified Mathieu functions.

The following return both function and first derivative:

.. autosummary::
   :toctree: generated/

   mathieu_cem     -- Even Mathieu function and its derivative.
   mathieu_sem     -- Odd Mathieu function and its derivative.
   mathieu_modcem1 -- Even modified Mathieu function of the first kind and its derivative.
   mathieu_modcem2 -- Even modified Mathieu function of the second kind and its derivative.
   mathieu_modsem1 -- Odd modified Mathieu function of the first kind and its derivative.
   mathieu_modsem2 -- Odd modified Mathieu function of the second kind and its derivative.

Spheroidal wave functions
-------------------------

.. autosummary::
   :toctree: generated/

   pro_ang1   -- Prolate spheroidal angular function of the first kind and its derivative.
   pro_rad1   -- Prolate spheroidal radial function of the first kind and its derivative.
   pro_rad2   -- Prolate spheroidal radial function of the second kind and its derivative.
   obl_ang1   -- Oblate spheroidal angular function of the first kind and its derivative.
   obl_rad1   -- Oblate spheroidal radial function of the first kind and its derivative.
   obl_rad2   -- Oblate spheroidal radial function of the second kind and its derivative.
   pro_cv     -- Characteristic value of prolate spheroidal function.
   obl_cv     -- Characteristic value of oblate spheroidal function.
   pro_cv_seq -- Characteristic values for prolate spheroidal wave functions.
   obl_cv_seq -- Characteristic values for oblate spheroidal wave functions.

The following functions require pre-computed characteristic value:

.. autosummary::
   :toctree: generated/

   pro_ang1_cv -- Prolate spheroidal angular function pro_ang1 for precomputed characteristic value.
   pro_rad1_cv -- Prolate spheroidal radial function pro_rad1 for precomputed characteristic value.
   pro_rad2_cv -- Prolate spheroidal radial function pro_rad2 for precomputed characteristic value.
   obl_ang1_cv -- Oblate spheroidal angular function obl_ang1 for precomputed characteristic value.
   obl_rad1_cv -- Oblate spheroidal radial function obl_rad1 for precomputed characteristic value.
   obl_rad2_cv -- Oblate spheroidal radial function obl_rad2 for precomputed characteristic value.

Kelvin functions
----------------

.. autosummary::
   :toctree: generated/

   kelvin       -- Kelvin functions as complex numbers.
   kelvin_zeros -- Compute nt zeros of all Kelvin functions.
   ber          -- Kelvin function ber.
   bei          -- Kelvin function bei
   berp         -- Derivative of the Kelvin function `ber`.
   beip         -- Derivative of the Kelvin function `bei`.
   ker          -- Kelvin function ker.
   kei          -- Kelvin function ker.
   kerp         -- Derivative of the Kelvin function ker.
   keip         -- Derivative of the Kelvin function kei.

The following functions do not accept NumPy arrays (they are not
universal functions):

.. autosummary::
   :toctree: generated/

   ber_zeros  -- Compute nt zeros of the Kelvin function ber(x).
   bei_zeros  -- Compute nt zeros of the Kelvin function bei(x).
   berp_zeros -- Compute nt zeros of the Kelvin function ber'(x).
   beip_zeros -- Compute nt zeros of the Kelvin function bei'(x).
   ker_zeros  -- Compute nt zeros of the Kelvin function ker(x).
   kei_zeros  -- Compute nt zeros of the Kelvin function kei(x).
   kerp_zeros -- Compute nt zeros of the Kelvin function ker'(x).
   keip_zeros -- Compute nt zeros of the Kelvin function kei'(x).

Combinatorics
-------------

.. autosummary::
   :toctree: generated/

   comb -- The number of combinations of N things taken k at a time.
   perm -- Permutations of N things taken k at a time, i.e., k-permutations of N.
   stirling2 -- Stirling numbers of the second kind.

Lambert W and related functions
-------------------------------

.. autosummary::
   :toctree: generated/

   lambertw    -- Lambert W function.
   wrightomega -- Wright Omega function.

Other special functions
-----------------------

.. autosummary::
   :toctree: generated/

   agm         -- Arithmetic, Geometric Mean.
   bernoulli   -- Bernoulli numbers B0..Bn (inclusive).
   binom       -- Binomial coefficient
   diric       -- Periodic sinc function, also called the Dirichlet function.
   euler       -- Euler numbers E0..En (inclusive).
   expn        -- Exponential integral E_n.
   exp1        -- Exponential integral E_1 of complex argument z.
   expi        -- Exponential integral Ei.
   factorial   -- The factorial of a number or array of numbers.
   factorial2  -- Double factorial.
   factorialk  -- Multifactorial of n of order k, n(!!...!).
   shichi      -- Hyperbolic sine and cosine integrals.
   sici        -- Sine and cosine integrals.
   softmax     -- Softmax function.
   log_softmax -- Logarithm of softmax function.
   spence      -- Spence's function, also known as the dilogarithm.
   zeta        -- Riemann zeta function.
   zetac       -- Riemann zeta function minus 1.
   softplus    -- Softplus function.

Convenience functions
---------------------

.. autosummary::
   :toctree: generated/

   cbrt      -- Cube root of `x`.
   exp10     -- 10**x.
   exp2      -- 2**x.
   radian    -- Convert from degrees to radians.
   cosdg     -- Cosine of the angle `x` given in degrees.
   sindg     -- Sine of angle given in degrees.
   tandg     -- Tangent of angle x given in degrees.
   cotdg     -- Cotangent of the angle `x` given in degrees.
   log1p     -- Calculates log(1+x) for use when `x` is near zero.
   expm1     -- ``exp(x) - 1`` for use when `x` is near zero.
   cosm1     -- ``cos(x) - 1`` for use when `x` is near zero.
   powm1     -- ``x**y - 1`` for use when `y` is near zero or `x` is near 1.
   round     -- Round to nearest integer.
   xlogy     -- Compute ``x*log(y)`` so that the result is 0 if ``x = 0``.
   xlog1py   -- Compute ``x*log1p(y)`` so that the result is 0 if ``x = 0``.
   logsumexp -- Compute the log of the sum of exponentials of input elements.
   exprel    -- Relative error exponential, (exp(x)-1)/x, for use when `x` is near zero.
   sinc      -- Return the sinc function.

