Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a7ux)

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.a7ux.01

Input Form

HypergeometricPFQ[{-(17/4)}, {9/2, 7/4}, -z] == (1/(247201320960 z^(7/2))) (Sqrt[Pi] z^(11/4) (54563590575 + 291005816400 z + 98023011840 z^2 + 7576657920 z^3 + 172687360 z^4 + 1048576 z^5) FresnelS[(2 z^(1/4))/Sqrt[Pi]] + 2 (4 Sqrt[z] (375921000 + 415303200 z + 1603929600 z^2 + 17208018405 z^3 + 6041909760 z^4 + 471544320 z^5 + 10780672 z^6 + 65536 z^7) Cos[2 Sqrt[z]] + (-751842000 + 171849600 z - 1833062400 z^2 + 13870739025 z^3 + 5720172480 z^4 + 463664640 z^5 + 10731520 z^6 + 65536 z^7) Sin[2 Sqrt[z]]))

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]