Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a7v5)

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=-17/4, b_1`>=-11/2

For fixed z and a₁=-17/4, b_1`=9/2

http://functions.wolfram.com/07.22.03.a7v5.01

Input Form

HypergeometricPFQ[{-(17/4)}, {9/2, 15/4}, -z] == (Sqrt[Pi] z^(3/4) (88229325959775 - 201667030765200 z + 293333862931200 z^2 + 521482422988800 z^3 + 87828618608640 z^4 + 4073211297792 z^5 + 61891149824 z^6 + 268435456 z^7) FresnelS[(2 z^(1/4))/Sqrt[Pi]] + 2 (4 Sqrt[z] (3079544832000 - 10829610484875 z + 13936804932960 z^2 + 31658527676160 z^3 + 5443099705344 z^4 + 253857300480 z^5 + 3865051136 z^6 + 16777216 z^7) Cos[2 Sqrt[z]] + (-6159089664000 + 461565201825 z + 1455947045280 z^2 + 28267387948800 z^3 + 5264349511680 z^4 + 251011203072 z^5 + 3852468224 z^6 + 16777216 z^7) Sin[2 Sqrt[z]]))/ (552292696719360 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]