# encoding: utf-8 # module scipy.special._gufuncs # from C:\Programs\Python\Python313\Lib\site-packages\scipy\special\_gufuncs.cp313-win_amd64.pyd # by generator 1.147 # no doc # no imports # functions def _lqmn(x, out1=None, out2=None, *args, **kwargs): # real signature unknown; NOTE: unreliably restored from __doc__ """ _lqmn(x[, out1, out2], / [, out=(None, None)], *, casting='same_kind', order='K', dtype=None, subok=True[, signature, axes, axis]) Sequence of associated Legendre functions of the second kind. Computes the associated Legendre function of the second kind of order m and degree n, ``Qmn(z)`` = :math:`Q_n^m(z)`, and its derivative, ``Qmn'(z)``. Returns two arrays of size ``(m+1, n+1)`` containing ``Qmn(z)`` and ``Qmn'(z)`` for all orders from ``0..m`` and degrees from ``0..n``. Parameters ---------- z : array_like Input value. Returns ------- Qmn_z : (m+1, n+1) array Values for all orders 0..m and degrees 0..n Qmn_d_z : (m+1, n+1) array Derivatives for all orders 0..m and degrees 0..n 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 """ pass def _lqn(x, out1=None, out2=None, *args, **kwargs): # real signature unknown; NOTE: unreliably restored from __doc__ """ _lqn(x[, out1, out2], / [, out=(None, None)], *, casting='same_kind', order='K', dtype=None, subok=True[, signature, axes, axis]) Legendre function of the second kind. Compute sequence of Legendre functions of the second kind, Qn(z) and derivatives for all degrees from 0 to n (inclusive). 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 """ pass def _rctj(x, out1=None, out2=None, *args, **kwargs): # real signature unknown; NOTE: unreliably restored from __doc__ """ _rctj(x[, out1, out2], / [, out=(None, None)], *, casting='same_kind', order='K', dtype=None, subok=True[, signature, axes, axis]) Compute Ricatti-Bessel function of the first kind and its derivative. The Ricatti-Bessel function of the first kind is defined as :math:`x j_n(x)`, where :math:`j_n` is the spherical Bessel function of the first kind of order :math:`n`. This function computes the value and first derivative of the Ricatti-Bessel function for all orders up to and including `n`. Parameters ---------- x : ndarray Argument at which to evaluate Returns ------- jn : ndarray Value of j0(x), ..., jn(x) jnp : ndarray First derivative j0'(x), ..., jn'(x) Notes ----- The computation is carried out via backward recurrence, using the relation DLMF 10.51.1 [2]_. Wrapper for a Fortran routine created by Shanjie Zhang and Jianming Jin [1]_. 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] NIST Digital Library of Mathematical Functions. https://dlmf.nist.gov/10.51.E1 """ pass def _rcty(x, out1=None, out2=None, *args, **kwargs): # real signature unknown; NOTE: unreliably restored from __doc__ """ _rcty(x[, out1, out2], / [, out=(None, None)], *, casting='same_kind', order='K', dtype=None, subok=True[, signature, axes, axis]) Compute Ricatti-Bessel function of the second kind and its derivative. The Ricatti-Bessel function of the second kind is defined as :math:`x y_n(x)`, where :math:`y_n` is the spherical Bessel function of the second kind of order :math:`n`. This function computes the value and first derivative of the function for all orders up to and including `n`. Parameters ---------- x : ndarray Argument at which to evaluate Returns ------- yn : ndarray Value of y0(x), ..., yn(x) ynp : ndarray First derivative y0'(x), ..., yn'(x) Notes ----- The computation is carried out via ascending recurrence, using the relation DLMF 10.51.1 [2]_. Wrapper for a Fortran routine created by Shanjie Zhang and Jianming Jin [1]_. 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] NIST Digital Library of Mathematical Functions. https://dlmf.nist.gov/10.51.E1 """ pass # no classes # variables with complex values assoc_legendre_p_all = { ( False, 0, ): None # (!) real value is "" , ( False, 1, ): None # (!) real value is "" , ( False, 2, ): None # (!) real value is "" , ( True, 0, ): None # (!) real value is "" , ( True, 1, ): None # (!) real value is "" , ( True, 2, ): None # (!) real value is "" , } legendre_p_all = ( None, # (!) real value is "" None, # (!) real value is "" None, # (!) real value is "" ) sph_harm_y_all = ( None, # (!) real value is "" None, # (!) real value is "" None, # (!) real value is "" ) sph_legendre_p_all = ( None, # (!) real value is "" None, # (!) real value is "" None, # (!) real value is "" ) __loader__ = None # (!) real value is '<_frozen_importlib_external.ExtensionFileLoader object at 0x000001B0161F3BF0>' __spec__ = None # (!) real value is "ModuleSpec(name='scipy.special._gufuncs', loader=<_frozen_importlib_external.ExtensionFileLoader object at 0x000001B0161F3BF0>, origin='C:\\\\Programs\\\\Python\\\\Python313\\\\Lib\\\\site-packages\\\\scipy\\\\special\\\\_gufuncs.cp313-win_amd64.pyd')"