Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.7979)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁},{b₁,b₂},z]

Specific values

For rational parameters with larger denominators and fixed z

For fixed z and a₁=-23/4, b_1`>=-11/2

For fixed z and a₁=-23/4, b_1`=-11/2

http://functions.wolfram.com/07.22.03.7979.01

Input Form

HypergeometricPFQ[{-(23/4)}, {-(11/2), 9/4}, -z] == (Sqrt[Pi] (61906053114675 + 256795479586800 z - 178640333625600 z^2 + 35817610752000 z^3 - 3473222860800 z^4 + 202078420992 z^5 - 8103395328 z^6 + 268435456 z^7) FresnelC[(2 z^(1/4))/Sqrt[Pi]] - 2 z^(1/4) ((61906053114675 + 14968002661920 z - 2514262705920 z^2 + 231340032000 z^3 - 13166641152 z^4 + 522190848 z^5 - 16777216 z^6) Cos[2 Sqrt[z]] + 4 Sqrt[z] (20635351038225 - 11731986937440 z + 2286286974720 z^2 - 219694841856 z^3 + 12731744256 z^4 - 509607936 z^5 + 16777216 z^6) Sin[2 Sqrt[z]]))/ (351588707205120 z^(5/4))

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,a₂},{b₁},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂},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]