Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.an2i)

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=9/2, a₂>=9/2

For fixed z and a₁=9/2, a₂=6, b₁>=-11/2

For fixed z and a₁=9/2, a₂=6, b₁=-7/2

http://functions.wolfram.com/07.25.03.an2i.01

Input Form

HypergeometricPFQ[{9/2, 6}, {-(7/2), -(1/2)}, z] == (1/165375) (165375 + 2551500 z - 39293100 z^2 + 302702400 z^3 - 4086482400 z^4 - 21073852800 z^5 - 28640539200 z^6 - 17360138880 z^7 - 5612758080 z^8 - 1053125920 z^9 - 119173740 z^10 - 8179360 z^11 - 330368 z^12 - 7168 z^13 - 64 z^14) - (1/165375) (2 E^z Sqrt[Pi] (4655851200 z^(9/2) + 15343146000 z^(11/2) + 17711769600 z^(13/2) + 9878761200 z^(15/2) + 3044290200 z^(17/2) + 554502165 z^(19/2) + 61553450 z^(21/2) + 4170520 z^(23/2) + 166960 z^(25/2) + 3600 z^(27/2) + 32 z^(29/2)) Erf[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]