Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9717)

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`=-11/2

http://functions.wolfram.com/07.22.03.9717.01

Input Form

HypergeometricPFQ[{-(17/4)}, {-(11/2), 19/4}, -z] == (Sqrt[Pi] (-84942397682517375 - 26714071015632000 z - 6476138428032000 z^2 - 2382027927552000 z^3 + 1905622342041600 z^4 - 232304437886976 z^5 + 12146637275136 z^6 - 328564998144 z^7 + 4294967296 z^8) FresnelS[(2 z^(1/4))/Sqrt[Pi]] + 2 z^(1/4) (4 Sqrt[z] (-28314132560839125 + 4038913117839600 z - 179892734112000 z^2 + 122195508277248 z^3 - 14670474706944 z^4 + 763125301248 z^5 - 20585644032 z^6 + 268435456 z^7) Cos[2 Sqrt[z]] + (84942397682517375 - 63891153179053200 z + 991979933817600 z^2 + 136334016000000 z^3 - 15315404783616 z^4 + 779407589376 z^5 - 20786970624 z^6 + 268435456 z^7) Sin[2 Sqrt[z]]))/ (3324923162394624 z^(15/4))

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]