Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.1724)

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=-11/2, a₂>=-11/2

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

For fixed z and a₁=-11/2, a₂=3, b₁=1

http://functions.wolfram.com/07.25.03.1724.01

Input Form

HypergeometricPFQ[{-(11/2), 3}, {1, 11/2}, -z] == (1/(100663296 z^4)) ((-7640325 + 4261950 z + 831600 z^2 - 2328480 z^3 + 78061728 z^4 + 136552512 z^5 + 61981440 z^6 + 10903040 z^7 + 795392 z^8 + 19968 z^9)/E^z) + (1/(201326592 z^(9/2))) (Sqrt[Pi] (7640325 - 9355500 z + 3367980 z^2 + 1995840 z^3 + 20956320 z^4 + 251475840 z^5 + 325987200 z^6 + 134120448 z^7 + 22581504 z^8 + 1610752 z^9 + 39936 z^10) 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]