Sergey B Kirpichev
fb69943530
Following functions kept: ```pycon >>> import inspect ... with_args = [] ... with_kwargs = [] ... for n in dir(mpmath): ... m = getattr(mpmath, n) ... try: ... s = inspect.signature(m) ... except: ... continue ... if any(_.kind == inspect._ParameterKind.VAR_POSITIONAL for _ in s.parameters.values()): ... for name in s.parameters: ... if s.parameters[name].kind == inspect._ParameterKind.VAR_POSITIONAL and name == 'args': ... with_args.append(n) ... break ... if any(_.kind == inspect._ParameterKind.VAR_KEYWORD for _ in s.parameters.values()): ... with_kwargs.append(n) ... print(with_args) ... print(with_kwargs) ... ['arange', 'ellipe', 'ellippi', 'linspace', 'matrix', 'ones', 'timing', 'zeros'] ['multiplicity', 'timing'] ``` We need support for multiple signatures in the first case. In the second - it's impossible to implement these functions without kwargs. Closes #1056
109 lines
2.3 KiB
ReStructuredText
109 lines
2.3 KiB
ReStructuredText
Bessel functions and related functions
|
|
--------------------------------------
|
|
|
|
The functions in this section arise as solutions to various differential
|
|
equations in physics, typically describing wavelike oscillatory behavior or a
|
|
combination of oscillation and exponential decay or growth. Mathematically,
|
|
they are special cases of the confluent hypergeometric functions `\,_0F_1`,
|
|
`\,_1F_1` and `\,_1F_2` (see :doc:`hypergeometric`).
|
|
|
|
|
|
Bessel functions
|
|
................
|
|
|
|
.. autofunction:: mpmath.besselj
|
|
.. autofunction:: mpmath.j0
|
|
.. autofunction:: mpmath.j1
|
|
.. autofunction:: mpmath.bessely
|
|
.. autofunction:: mpmath.besseli
|
|
.. autofunction:: mpmath.besselk
|
|
|
|
|
|
Bessel function zeros
|
|
.....................
|
|
|
|
.. autofunction:: mpmath.besseljzero
|
|
.. autofunction:: mpmath.besselyzero
|
|
|
|
|
|
Hankel functions
|
|
................
|
|
|
|
.. autofunction:: mpmath.hankel1
|
|
.. autofunction:: mpmath.hankel2
|
|
|
|
|
|
Spherical Bessel functions
|
|
..........................
|
|
|
|
.. autofunction:: mpmath.spherical_jn
|
|
.. autofunction:: mpmath.spherical_yn
|
|
.. autofunction:: mpmath.spherical_in
|
|
.. autofunction:: mpmath.spherical_kn
|
|
|
|
|
|
Kelvin functions
|
|
................
|
|
|
|
.. autofunction:: mpmath.ber
|
|
.. autofunction:: mpmath.bei
|
|
.. autofunction:: mpmath.ker
|
|
.. autofunction:: mpmath.kei
|
|
|
|
|
|
Struve functions
|
|
................
|
|
|
|
.. autofunction:: mpmath.struveh
|
|
.. autofunction:: mpmath.struvel
|
|
|
|
|
|
Anger-Weber functions
|
|
.....................
|
|
|
|
.. autofunction:: mpmath.angerj
|
|
.. autofunction:: mpmath.webere
|
|
|
|
|
|
Lommel functions
|
|
................
|
|
|
|
.. autofunction:: mpmath.lommels1
|
|
.. autofunction:: mpmath.lommels2
|
|
|
|
|
|
Airy and Scorer functions
|
|
.........................
|
|
|
|
.. autofunction:: mpmath.airyai
|
|
.. autofunction:: mpmath.airybi
|
|
.. autofunction:: mpmath.airyaizero
|
|
.. autofunction:: mpmath.airybizero
|
|
.. autofunction:: mpmath.scorergi
|
|
.. autofunction:: mpmath.scorerhi
|
|
|
|
|
|
Coulomb wave functions
|
|
......................
|
|
|
|
.. autofunction:: mpmath.coulombf
|
|
.. autofunction:: mpmath.coulombg
|
|
.. autofunction:: mpmath.coulombc
|
|
|
|
|
|
Confluent U and Whittaker functions
|
|
...................................
|
|
|
|
.. autofunction:: mpmath.hyperu
|
|
.. autofunction:: mpmath.whitm
|
|
.. autofunction:: mpmath.whitw
|
|
|
|
|
|
Parabolic cylinder functions
|
|
............................
|
|
|
|
.. autofunction:: mpmath.pcfd
|
|
.. autofunction:: mpmath.pcfu
|
|
.. autofunction:: mpmath.pcfv
|
|
.. autofunction:: mpmath.pcfw
|