Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a8b7)

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=-15/4, b_1`>=-11/2

For fixed z and a₁=-15/4, b_1`=9/2

http://functions.wolfram.com/07.22.03.a8b7.01

Input Form

HypergeometricPFQ[{-(15/4)}, {9/2, 17/4}, -z] == (Sqrt[Pi] z^(1/4) (-23609013553125 + 58760211510000 z - 62677558944000 z^2 + 128569351680000 z^3 + 40335482880000 z^4 + 2634153984000 z^5 + 51086622720 z^6 + 268435456 z^7) FresnelC[(2 z^(1/4))/Sqrt[Pi]] - 2 ((-Sqrt[z]) (6441596209125 - 6117534007200 z + 6183391737600 z^2 + 2377855549440 z^3 + 161703198720 z^4 + 3177185280 z^5 + 16777216 z^6) Cos[2 Sqrt[z]] + 4 (-2145927168000 + 4719768201225 z - 4719564511200 z^2 + 7622844768000 z^3 + 2491365703680 z^4 + 164042833920 z^5 + 3189768192 z^6 + 16777216 z^7) Sin[2 Sqrt[z]]))/ (104216710348800 z^(7/2))

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]