Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.ag0n)

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=21/4, b_1`>=-11/2

For fixed z and a₁=21/4, b_1`=-7/2

http://functions.wolfram.com/07.22.03.ag0n.01

Input Form

HypergeometricPFQ[{21/4}, {-(7/2), 23/4}, -z] == (209 (2 Sqrt[z] (5771092201875 - 6688804122000 z + 1549128672000 z^2 - 169660108800 z^3 + 11625758720 z^4 - 655360000 z^5 + 16777216 z^6) BesselJ[-(1/4), Sqrt[z]]^2 + (-17313276605625 + 46448548146000 z - 16585968672000 z^2 + 2416587264000 z^3 - 199453900800 z^4 + 11917066240 z^5 - 553648128 z^6) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] - 2 Sqrt[z] (17313276605625 - 9513558054000 z + 1918567123200 z^2 - 198832435200 z^3 + 13329039360 z^4 - 728760320 z^5 + 16777216 z^6) BesselJ[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/ (13904117760 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]