Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.anc7)

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=5, a₂>=5

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

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

http://functions.wolfram.com/07.25.03.anc7.01

Input Form

HypergeometricPFQ[{5, 11/2}, {-(11/2), 5/2}, -z] == (1/9823275) (9823275 + 19646550 z + 24324300 z^2 + 27027000 z^3 + 33415200 z^4 + 58605120 z^5 + 273490560 z^6 - 357089040 z^7 + 151295760 z^8 - 30474840 z^9 + 3261576 z^10 - 188784 z^11 + 5536 z^12 - 64 z^13) + (1/9823275) ((4 Sqrt[Pi] z^(13/2) (-100727550 + 105204330 z - 41278545 z^2 + 8004465 z^3 - 838320 z^4 + 47880 z^5 - 1392 z^6 + 16 z^7) 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]