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

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=1/2, a₂>=1/2

For fixed z and a₁=1/2, a₂=5, b₁>=-11/2

For fixed z and a₁=1/2, a₂=5, b₁=-11/2

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

Input Form

HypergeometricPFQ[{1/2, 5}, {-(11/2), -(3/2)}, -z] == (1/93555) (93555 - 28350 z + 56700 z^2 + 189000 z^3 + 352800 z^4 + 762048 z^5 + 3991680 z^6 - 5911560 z^7 + 2570688 z^8 - 490044 z^9 + 45256 z^10 - 1968 z^11 + 32 z^12) - (1/93555) ((2 Sqrt[Pi] (3052350 z^(13/2) - 3500028 z^(15/2) + 1397697 z^(17/2) - 255864 z^(19/2) + 23112 z^(21/2) - 992 z^(23/2) + 16 z^(25/2)) 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]