Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.aji7)

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=5/2, a₂>=5/2

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

For fixed z and a₁=5/2, a₂=5, b₁=-5/2

http://functions.wolfram.com/07.25.03.aji7.01

Input Form

HypergeometricPFQ[{5/2, 5}, {-(5/2), -(3/2)}, z] == (1/405) (405 + 1350 z + 18900 z^2 - 793800 z^3 - 7009200 z^4 - 11613888 z^5 - 7272720 z^6 - 2151480 z^7 - 329022 z^8 - 26436 z^9 - 1048 z^10 - 16 z^11) + (1/405) E^z Sqrt[Pi] (-2316600 z^(7/2) - 10810800 z^(9/2) - 14484600 z^(11/2) - 8212500 z^(13/2) - 2304009 z^(15/2) - 341736 z^(17/2) - 26952 z^(19/2) - 1056 z^(21/2) - 16 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]