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

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=2, a₂>=2

For fixed z and a₁=2, a₂=5/2, b₁>=-11/2

For fixed z and a₁=2, a₂=5/2, b₁=-11/2

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

Input Form

HypergeometricPFQ[{2, 5/2}, {-(11/2), -(3/2)}, z] == (1/93555) (93555 + 56700 z + 132300 z^2 - 453600 z^3 + 831600 z^4 - 1729728 z^5 + 8648640 z^6 + 11535360 z^7 + 4332288 z^8 + 666624 z^9 + 44032 z^10 + 1024 z^11) + (1/93555) (512 E^z Sqrt[Pi] (25200 z^(13/2) + 26208 z^(15/2) + 9072 z^(17/2) + 1344 z^(19/2) + 87 z^(21/2) + 2 z^(23/2)) 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]