Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.8450)

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=6, b₁>=-11/2

For fixed z and a₁=-7/2, a₂=6, b₁=1

http://functions.wolfram.com/07.25.03.8450.01

Input Form

HypergeometricPFQ[{-(7/2), 6}, {1, 11/2}, -z] == (1/(134217728 z^4)) ((9 (-25725 - 42350 z - 58940 z^2 - 141960 z^3 + 12358544 z^4 + 26710112 z^5 + 10296000 z^6 + 933504 z^7))/E^z) + (1/(268435456 z^(9/2))) (9 Sqrt[Pi] (25725 + 25200 z + 35280 z^2 + 109760 z^3 + 2469600 z^4 + 43464960 z^5 + 62782720 z^6 + 21525504 z^7 + 1867008 z^8) 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]