Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.afe3)

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.afe3.01

Input Form

HypergeometricPFQ[{17/4}, {9/2, -(21/4)}, -z] == (1/(74468160 Sqrt[2] z^(11/4))) ((-4 z (-73931059125 + 23657938920 z - 3402570240 z^2 + 383365120 z^3 - 32178176 z^4 + 524288 z^5) BesselJ[-(1/4), Sqrt[z]]^2 + 4 Sqrt[z] (-221793177375 + 113220136260 z - 21476067840 z^2 + 2521528320 z^3 - 263716864 z^4 + 11796480 z^5) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] + (665379532125 - 466399367280 z + 122541582240 z^2 - 16753950720 z^3 + 1837547520 z^4 - 141033472 z^5 + 2097152 z^6) BesselJ[3/4, Sqrt[z]]^2) Gamma[3/4]^2)

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]