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

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=5/2, a₂>=5/2

For fixed z and a₁=5/2, a₂=6, b₁>=-11/2

For fixed z and a₁=5/2, a₂=6, b₁=-7/2

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

Input Form

HypergeometricPFQ[{5/2, 6}, {-(7/2), -(3/2)}, -z] == (1/14175) (14175 - 40500 z + 396900 z^2 + 6350400 z^3 + 104781600 z^4 - 590887440 z^5 + 798220800 z^6 - 456068520 z^7 + 133256880 z^8 - 21665130 z^9 + 2019816 z^10 - 106320 z^11 + 2912 z^12 - 32 z^13) + (1/14175) ((Sqrt[Pi] (-249420600 z^(9/2) + 861634800 z^(11/2) - 979368300 z^(13/2) + 513957600 z^(15/2) - 143199675 z^(17/2) + 22625370 z^(19/2) - 2071560 z^(21/2) + 107760 z^(23/2) - 2928 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]