Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a7u1)

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`=7/2

http://functions.wolfram.com/07.22.03.a7u1.01

Input Form

HypergeometricPFQ[{-(17/4)}, {7/2, 23/4}, -z] == (Sqrt[Pi] (7044115540336875 + 13524701837446800 z + 78689174326963200 z^2 - 139891865470156800 z^3 + 159876417680179200 z^4 + 232547516625715200 z^5 + 33073424586768384 z^6 + 1326252615008256 z^7 + 17742509899776 z^8 + 68719476736 z^9) FresnelS[(2 z^(1/4))/Sqrt[Pi]] + 2 z^(1/4) (4 Sqrt[z] (2348038513445625 + 3434844911097600 z - 7949073172884480 z^2 + 7936192335052800 z^3 + 14177957382586368 z^4 + 2051990938976256 z^5 + 82684630007808 z^6 + 1108101562368 z^7 + 4294967296 z^8) Cos[2 Sqrt[z]] + (-7044115540336875 - 6010978594420800 z - 1588336838000640 z^2 + 1788938388357120 z^3 + 12867980732006400 z^4 + 1993330648940544 z^5 + 81867042717696 z^6 + 1104880336896 z^7 + 4294967296 z^8) Sin[2 Sqrt[z]]))/(258097160480882688 z^(19/4))

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]