Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9575)

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=-19/4, b_1`>=-11/2

For fixed z and a₁=-19/4, b_1`=7/2

http://functions.wolfram.com/07.22.03.9575.01

Input Form

HypergeometricPFQ[{-(19/4)}, {7/2, 21/4}, -z] == (Sqrt[Pi] (-17494279042865625 - 64594261081350000 z + 459336967689600000 z^2 - 685943205083136000 z^3 + 1829181880221696000 z^4 + 750433591885824000 z^5 + 67265756135424000 z^6 + 1996757139456000 z^7 + 21298742820864 z^8 + 68719476736 z^9) FresnelC[(2 z^(1/4))/Sqrt[Pi]] + 2 z^(1/4) ((17494279042865625 + 45933696768960000 z - 65428463376460800 z^2 + 82398544994304000 z^3 + 43379764606402560 z^4 + 4091884465029120 z^5 + 123565202472960 z^6 + 1327144894464 z^7 + 4294967296 z^8) Cos[2 Sqrt[z]] - 4 Sqrt[z] (-5831426347621875 + 38393106857582400 z - 52629602415667200 z^2 + 106975841185382400 z^3 + 46161769855057920 z^4 + 4181245349068800 z^5 + 124549488181248 z^6 + 1330366119936 z^7 + 4294967296 z^8) Sin[2 Sqrt[z]]))/ (1581936098358067200 z^(17/4))

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]