hypergeo2
http://www.openxm.org/...
2003-08-11
2002-08-11, 2003-11-30
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This CD defines some famous hypergeometric functions such as
Bessel functions and Airy functions.
These functions are described in the following books.
(1) Handbook of Mathematical Functions, Abramowitz, Stegun
(2) Higher transcendental functions. Krieger Publishing Co., Inc., Melbourne, Fla., 1981, Erdlyi, Arthur; Magnus, Wilhelm; Oberhettinger, Fritz; Tricomi, Francesco G.
kummer
Kummer's hypergeometric function.
kummer(a,c;z) = hypergeo1.hypergeometric1F1(a,c;z)
besselJ
The Bessel function.
This function is one of the famous two solutions of the Bessel
differential equation at z=0.
besselJ(v,z)
= (\frac{z}{2})^v \sum_{n=0}^{+\infty}
\frac{(-1)^n}{n! \Gamma(v+n+1)} (\frac{z}{2})^2n
2
0
1
1
2
2
2
2
2
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besselY
The Bessel function.
This function is the another one of the famous two solutions of the Bessel
differential equation at z=0.
besselY(v,z)
= (\cos(v \pi) besselJ(v,z) - besselJ(-v,z))/\sin(v \pi)
2
2
2
0
hankel1
The first Hankel function.
This function is one of the famous two solutions of the Bessel
differential equation at z=\infty.
hankel1(v,z)
= besselJ(v,z) + i BesselY(v,z)
hankel2
The second Hankel function.
This function is the another one of the famous two solutions of the Bessel
differential equation at z=\infty.
hankel2(v,z)
= besselJ(v,z) - i BesselY(v,z)
airyAi
The first Airy function.
This function is one of the famous two solutions of the Airy
differential equation, and converges to 0 when z->\infty
(\frac{d^2}{dz^2} - z) airyAi(z) = 0
0
airyBi
The second Airy function.
This function is the another one of the famous two solutions of the Airy
differential equation, and diverges when z->\infty
(\frac{d^2}{dz^2} - z) airyBi(z) = 0
0