Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9755)

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/07.22.03.9755.01

Input Form

HypergeometricPFQ[{-(17/4)}, {-(9/2), 9/4}, -z] == ((2 Sqrt[z] (13082700015 + 11232864720 z - 3957972480 z^2 + 483631104 z^3 - 29949952 z^4 + 1048576 z^5) BesselJ[1/4, Sqrt[z]]^2 - 3 (-5019589575 + 15681813840 z - 4432243200 z^2 + 511385600 z^3 - 30867456 z^4 + 1048576 z^5) BesselJ[1/4, Sqrt[z]] BesselJ[5/4, Sqrt[z]] + 2 Sqrt[z] (-15058768725 + 14792999760 z - 4353338880 z^2 + 507125760 z^3 - 30736384 z^4 + 1048576 z^5) BesselJ[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/(16094453760 Sqrt[2] z^(3/4))

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]