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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 | )abbrev category SPFCAT SpecialFunctionCategory
++ Author: Manuel Bronstein
++ Date Last Updated: 11 May 1993
++ Description:
++ Category for the other special functions;
SpecialFunctionCategory() : Category == SIG where
SIG ==> with
abs : $ -> $
++ abs(x) returns the absolute value of x.
Gamma : $ -> $
++ Gamma(x) is the Euler Gamma function.
Beta : ($,$)->$
++ Beta(x,y) is \spad{Gamma(x) * Gamma(y)/Gamma(x+y)}.
digamma : $ -> $
++ digamma(x) is the logarithmic derivative of \spad{Gamma(x)}
++ (often written \spad{psi(x)} in the literature).
polygamma : ($, $) -> $
++ polygamma(k,x) is the \spad{k-th} derivative of \spad{digamma(x)},
++ (often written \spad{psi(k,x)} in the literature).
Gamma : ($, $) -> $
++ Gamma(a,x) is the incomplete Gamma function.
besselJ : ($,$) -> $
++ besselJ(v,z) is the Bessel function of the first kind.
besselY : ($,$) -> $
++ besselY(v,z) is the Bessel function of the second kind.
besselI : ($,$) -> $
++ besselI(v,z) is the modified Bessel function of the first kind.
besselK : ($,$) -> $
++ besselK(v,z) is the modified Bessel function of the second kind.
airyAi : $ -> $
++ airyAi(x) is the Airy function \spad{Ai(x)}.
airyBi : $ -> $
++ airyBi(x) is the Airy function \spad{Bi(x)}.
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