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

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=1/2, a₂>=1/2

For fixed z and a₁=1/2, a₂=3, b₁>=-11/2

For fixed z and a₁=1/2, a₂=3, b₁=-11/2

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

Input Form

HypergeometricPFQ[{1/2, 3}, {-(11/2), -(3/2)}, z] == (1/31185) (31185 + 5670 z + 7560 z^2 - 18000 z^3 + 25200 z^4 - 42336 z^5 + 177408 z^6 + 169344 z^7 + 43776 z^8 + 4160 z^9 + 128 z^10) + (32 E^z Sqrt[Pi] (7650 z^(13/2) + 5916 z^(15/2) + 1431 z^(17/2) + 132 z^(19/2) + 4 z^(21/2)) Erf[Sqrt[z]])/31185

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]