Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.an8i)

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=5, b₁>=-11/2

For fixed z and a₁=5, a₂=5, b₁=-7/2

http://functions.wolfram.com/07.25.03.an8i.01

Input Form

HypergeometricPFQ[{5, 5}, {-(7/2), 4}, -z] == (1/10080) (10080 + 18000 z + 25920 z^2 + 47040 z^3 + 215040 z^4 - 251007 z^5 + 85120 z^6 - 12016 z^7 + 736 z^8 - 16 z^9) + (1/20160) ((Sqrt[Pi] (-619905 z^(9/2) + 576810 z^(11/2) - 181560 z^(13/2) + 24752 z^(15/2) - 1488 z^(17/2) + 32 z^(19/2)) 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]