Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.ae7b)

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=13/4, b_1`>=-11/2

For fixed z and a₁=13/4, b_1`=-9/2

http://functions.wolfram.com/07.22.03.ae7b.01

Input Form

HypergeometricPFQ[{13/4}, {-(9/2), 23/4}, -z] == -((209 (10 Sqrt[z] (-14235360764625 + 15653400562800 z - 2852856115200 z^2 + 204922798080 z^3 - 6513229824 z^4 + 71303168 z^5) BesselJ[-(1/4), Sqrt[z]]^2 + (213530411469375 - 560180683062000 z + 170706227328000 z^2 - 18123691622400 z^3 + 847415869440 z^4 - 16609443840 z^5 + 67108864 z^6) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] - 6 Sqrt[z] (-71176803823125 + 34883046198000 z - 5623020748800 z^2 + 380044492800 z^3 - 11578900480 z^4 + 121634816 z^5) BesselJ[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/ (4529848320 Sqrt[2] z^(17/4)))

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]