Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8313)

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=-23/4, b_1`>=-11/2

For fixed z and a₁=-23/4, b_1`=3/2

http://functions.wolfram.com/07.22.03.8313.01

Input Form

HypergeometricPFQ[{-(23/4)}, {3/2, 7/4}, -z] == ((2 Sqrt[z] (32739038206875 + 105719548334400 z + 51200373369600 z^2 + 6466309324800 z^3 + 269370327040 z^4 + 3921674240 z^5 + 16777216 z^6) BesselJ[-(1/4), Sqrt[z]]^2 - (7905853580625 + 82001626106400 z + 47568384864000 z^2 + 6304344883200 z^3 + 266947461120 z^4 + 3911188480 z^5 + 16777216 z^6) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] + 2 Sqrt[z] (18285774281775 + 95017072550400 z + 49682112480000 z^2 + 6400467763200 z^3 + 268396462080 z^4 + 3917479936 z^5 + 16777216 z^6) BesselJ[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/ (60207507360000 Sqrt[2] z^(1/4))

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]