Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.anl1)

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=6, b₁>=-11/2

For fixed z and a₁=5, a₂=6, b₁=1

http://functions.wolfram.com/07.25.03.anl1.01

Input Form

HypergeometricPFQ[{5, 6}, {1, 5/2}, z] == (1/(983040 z)) (-1575 + 884340 z + 6917760 z^2 + 11003280 z^3 + 6389600 z^4 + 1663680 z^5 + 207872 z^6 + 12032 z^7 + 256 z^8) + (1/(1966080 z^(3/2))) (E^z Sqrt[Pi] (1575 + 97650 z + 4813200 z^2 + 21151200 z^3 + 27152160 z^4 + 14262720 z^5 + 3523840 z^6 + 427520 z^7 + 24320 z^8 + 512 z^9) 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]