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109 lines
2.3 KiB
ReStructuredText
109 lines
2.3 KiB
ReStructuredText
Bessel functions and related functions
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The functions in this section arise as solutions to various differential
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equations in physics, typically describing wavelike oscillatory behavior or a
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combination of oscillation and exponential decay or growth. Mathematically,
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they are special cases of the confluent hypergeometric functions `\,_0F_1`,
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`\,_1F_1` and `\,_1F_2` (see :doc:`hypergeometric`).
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Bessel functions
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................
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.. autofunction:: mpmath.besselj
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.. autofunction:: mpmath.j0
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.. autofunction:: mpmath.j1
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.. autofunction:: mpmath.bessely
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.. autofunction:: mpmath.besseli
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.. autofunction:: mpmath.besselk
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Bessel function zeros
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.....................
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.. autofunction:: mpmath.besseljzero
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.. autofunction:: mpmath.besselyzero
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Hankel functions
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................
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.. autofunction:: mpmath.hankel1
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.. autofunction:: mpmath.hankel2
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Spherical Bessel functions
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..........................
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.. autofunction:: mpmath.spherical_jn
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.. autofunction:: mpmath.spherical_yn
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.. autofunction:: mpmath.spherical_in
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.. autofunction:: mpmath.spherical_kn
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Kelvin functions
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................
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.. autofunction:: mpmath.ber
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.. autofunction:: mpmath.bei
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.. autofunction:: mpmath.ker
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.. autofunction:: mpmath.kei
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Struve functions
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................
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.. autofunction:: mpmath.struveh
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.. autofunction:: mpmath.struvel
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Anger-Weber functions
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.....................
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.. autofunction:: mpmath.angerj
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.. autofunction:: mpmath.webere
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Lommel functions
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................
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.. autofunction:: mpmath.lommels1
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.. autofunction:: mpmath.lommels2
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Airy and Scorer functions
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.........................
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.. autofunction:: mpmath.airyai
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.. autofunction:: mpmath.airybi
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.. autofunction:: mpmath.airyaizero
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.. autofunction:: mpmath.airybizero
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.. autofunction:: mpmath.scorergi
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.. autofunction:: mpmath.scorerhi
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Coulomb wave functions
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......................
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.. autofunction:: mpmath.coulombf
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.. autofunction:: mpmath.coulombg
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.. autofunction:: mpmath.coulombc
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Confluent U and Whittaker functions
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...................................
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.. autofunction:: mpmath.hyperu(a, b, z)
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.. autofunction:: mpmath.whitm(k,m,z)
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.. autofunction:: mpmath.whitw(k,m,z)
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Parabolic cylinder functions
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............................
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.. autofunction:: mpmath.pcfd
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.. autofunction:: mpmath.pcfu
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.. autofunction:: mpmath.pcfv
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.. autofunction:: mpmath.pcfw
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