Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.ad1m)

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=2, b₁>=-11/2

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

http://functions.wolfram.com/07.25.03.ad1m.01

Input Form

HypergeometricPFQ[{1/2, 2}, {-(11/2), -(5/2)}, z] == (1/155925) (155925 + 11340 z + 3780 z^2 + 7200 z^3 - 25200 z^4 + 60480 z^5 - 310464 z^6 - 396288 z^7 - 126720 z^8 - 14336 z^9 - 512 z^10) - (256 E^z Sqrt[Pi] (1800 z^(13/2) + 1770 z^(15/2) + 522 z^(17/2) + 57 z^(19/2) + 2 z^(21/2)) Erf[Sqrt[z]])/155925

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]