Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.7983)

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/07.22.03.7983.01

Input Form

HypergeometricPFQ[{-(23/4)}, {-(11/2), 13/4}, -z] == (Sqrt[Pi] (9595438232774625 + 7923974798678400 z + 16434910693555200 z^2 - 7621987568025600 z^3 + 1146163544064000 z^4 - 88914505236480 z^5 + 4311006314496 z^6 - 148176371712 z^7 + 4294967296 z^8) FresnelC[(2 z^(1/4))/Sqrt[Pi]] - 2 z^(1/4) ((9595438232774625 - 2311159316281200 z + 581324599215360 z^2 - 78286345482240 z^3 + 5852797009920 z^4 - 279111008256 z^5 + 9512681472 z^6 - 268435456 z^7) Cos[2 Sqrt[z]] + 4 Sqrt[z] (3198479410924875 + 1179162916470000 z - 493222973886720 z^2 + 72819505704960 z^3 - 5612155895808 z^4 + 271284436992 z^5 - 9311354880 z^6 + 268435456 z^7) Sin[2 Sqrt[z]]))/ (20001490898780160 z^(9/4))

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]