mma` is the gamma function and :math:`J_v` is the Bessel function of the first kind. Parameters ---------- v : float Order of the Lambda function x : float Value at which to evaluate the function and derivatives Returns ------- vl : ndarray Values of Lambda_vi(x), for vi=v-int(v), vi=1+v-int(v), ..., vi=v. dl : ndarray Derivatives Lambda_vi'(x), for vi=v-int(v), vi=1+v-int(v), ..., vi=v. References ---------- .. [1] Zhang, Shanjie and Jin, Jianming. "Computation of Special Functions", John Wiley and Sons, 1996. https://people.sc.fsu.edu/~jburkardt/f77_src/special_functions/special_functions.html .. [2] Jahnke, E. and Emde, F. "Tables of Functions with Formulae and Curves" (4th ed.), Dover, 1945 rÍ