Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.anuf)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]

Specific values

For integer and half-integer parameters and fixed z

For fixed z and a₁=11/2, a₂>=11/2

For fixed z and a₁=11/2, a₂=6, b₁>=-11/2

For fixed z and a₁=11/2, a₂=6, b₁=-3/2

http://functions.wolfram.com/07.25.03.anuf.01

Input Form

HypergeometricPFQ[{11/2, 6}, {-(3/2), -(1/2)}, -z] == (1/42525) (42525 - 1871100 z - 170270100 z^2 + 3178375200 z^3 - 10378368000 z^4 + 12655122480 z^5 - 7470655920 z^6 + 2424000780 z^7 - 462449340 z^8 + 53537610 z^9 - 3770088 z^10 + 156432 z^11 - 3488 z^12 + 32 z^13) + (1/42525) ((Sqrt[Pi] (681080400 z^(5/2) - 5935129200 z^(7/2) + 14675661000 z^(9/2) - 15574923000 z^(11/2) + 8503951050 z^(13/2) - 2632518630 z^(15/2) + 487513215 z^(17/2) - 55348650 z^(19/2) + 3846600 z^(21/2) - 158160 z^(23/2) + 3504 z^(25/2) - 32 z^(27/2)) Erfi[Sqrt[z]])/E^z)

Standard Form

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MathML Form

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Rule Form

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Date Added to functions.wolfram.com (modification date)

2007-05-02

HypergeometricPFQ[{},{},z]
HypergeometricPFQ[{},{b},z]
HypergeometricPFQ[{a},{},z]
HypergeometricPFQ[{a},{b},z]
HypergeometricPFQ[{a₁},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅},{b₁,b₂,b₃,b₄},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅,a₆},{b₁,b₂,b₃,b₄,b₅},z]
HypergeometricPFQ[{a₁,...,a_p},{b₁,...,b_q},z]