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

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=4, b₁>=-11/2

For fixed z and a₁=1/2, a₂=4, b₁=-11/2

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

Input Form

HypergeometricPFQ[{1/2, 4}, {-(11/2), -(9/2)}, -z] == (1/29469825) (29469825 - 2381400 z + 567000 z^2 - 324000 z^3 + 529200 z^4 - 5080320 z^5 - 167650560 z^6 + 1182643200 z^7 - 1629930240 z^8 + 868976640 z^9 - 222409728 z^10 + 29784576 z^11 - 2115840 z^12 + 74752 z^13 - 1024 z^14) + (1/29469825) ((128 Sqrt[Pi] (3488400 z^(13/2) - 13604760 z^(15/2) + 15485760 z^(17/2) - 7559460 z^(19/2) + 1846350 z^(21/2) - 240675 z^(23/2) + 16818 z^(25/2) - 588 z^(27/2) + 8 z^(29/2)) 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]