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. é