Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9021)

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=-21/4, b_1`>=-11/2

For fixed z and a₁=-21/4, b_1`=9/2

http://functions.wolfram.com/07.22.03.9021.01

Input Form

HypergeometricPFQ[{-(21/4)}, {9/2, -(5/4)}, -z] == (1/(811129334400 z^(7/2))) (2 Sqrt[z] (-618718975875 - 43418875500 z - 92626934400 z^2 + 48088857600 z^3 - 39264583680 z^4 + 271755509760 z^5 + 37864243200 z^6 + 1154482176 z^7 + 8388608 z^8) Cos[2 Sqrt[z]] + 8192 Sqrt[Pi] z^(23/4) (135958095 + 18592560 z + 564480 z^2 + 4096 z^3) FresnelS[(2 z^(1/4))/Sqrt[Pi]] + (618718975875 - 781539759000 z - 185253868800 z^2 + 134730086400 z^3 - 77104742400 z^4 + 123367587840 z^5 + 18512363520 z^6 + 574095360 z^7 + 4194304 z^8) 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]