Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.7288)

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=-7/2, a₂>=-7/2

For fixed z and a₁=-7/2, a₂=3, b₁>=-11/2

For fixed z and a₁=-7/2, a₂=3, b₁=7/2

http://functions.wolfram.com/07.25.03.7288.01

Input Form

HypergeometricPFQ[{-(7/2), 3}, {7/2, 5}, z] == (8 (1 + 5 z))/(143 z^4) + (1/(549120 z^4)) (E^z (-30720 - 122880 z - 86985 z^2 - 101710 z^3 + 247400 z^4 - 86224 z^5 + 9904 z^6 - 352 z^7)) + (1/(1098240 z^(5/2))) (Sqrt[Pi] (225225 + 180180 z + 386100 z^2 - 572000 z^3 + 182000 z^4 - 20160 z^5 + 704 z^6) Erfi[Sqrt[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]