Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a8al)

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=-15/4, b_1`>=-11/2

For fixed z and a₁=-15/4, b_1`=9/2

http://functions.wolfram.com/07.22.03.a8al.01

Input Form

HypergeometricPFQ[{-(15/4)}, {9/2, -(5/4)}, -z] == ((4 z (1140591375 + 370477800 z + 572083200 z^2 - 520243200 z^3 + 380436480 z^4 + 85852160 z^5 + 2097152 z^6) BesselJ[-(1/4), Sqrt[z]]^ 2 - 4 Sqrt[z] (3421774125 + 459666900 z + 432432000 z^2 - 319104000 z^3 + 165150720 z^4 + 42270720 z^5 + 1048576 z^6) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] + (10265322375 - 576298800 z + 933055200 z^2 + 2927232000 z^3 - 2342707200 z^4 + 1439170560 z^5 + 341311488 z^6 + 8388608 z^7) BesselJ[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/(1384344000 Sqrt[2] z^(11/4))

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]