Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a9pz)

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=-7/4, b_1`>=-11/2

For fixed z and a₁=-7/4, b_1`=-11/2

http://functions.wolfram.com/07.22.03.a9pz.01

Input Form

HypergeometricPFQ[{-(7/4)}, {-(11/2), 21/4}, -z] == (221 (11 Sqrt[Pi] (6133589505225 + 1161389728800 z + 147478060800 z^2 + 20298055680 z^3 + 9021358080 z^4 - 836763648 z^5 + 16777216 z^6) FresnelC[(2 z^(1/4))/Sqrt[Pi]] - 2 z^(1/4) ((67469484557475 - 59192163177840 z + 6272733519360 z^2 - 91341250560 z^3 + 586088448 z^4 - 11534336 z^5) Cos[2 Sqrt[z]] + 4 Sqrt[z] (22489828185825 - 6022635307920 z + 255628638720 z^2 + 5509472256 z^3 - 577437696 z^4 + 11534336 z^5) Sin[2 Sqrt[z]])))/ (18141941858304 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]