chore: import upstream snapshot with attribution

2026-07-13 12:32:53 +08:00
commit 2a16f2f53b
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+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(a, b, z)
+.. autofunction:: mpmath.whitm(k,m,z)
+.. autofunction:: mpmath.whitw(k,m,z)
+
+
+Parabolic cylinder functions
+............................
+
+.. autofunction:: mpmath.pcfd
+.. autofunction:: mpmath.pcfu
+.. autofunction:: mpmath.pcfv
+.. autofunction:: mpmath.pcfw