Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.ab0r)

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=-1/4, b_1`>=-11/2

For fixed z and a₁=-1/4, b_1`=-11/2

http://functions.wolfram.com/07.22.03.ab0r.01

Input Form

HypergeometricPFQ[{-(1/4)}, {-(11/2), -(23/4)}, -z] == (1/(15740160975 z^(1/4))) (Sqrt[2] ((15740160975 + 31604750100 z + 10740114000 z^2 - 4918193280 z^3 + 640620288 z^4 - 41115648 z^5 + 1507328 z^6) BesselJ[1/4, Sqrt[z]]^2 + 4 Sqrt[z] (-15740160975 - 10617868800 z + 7414545600 z^2 - 1302174720 z^3 + 106240512 z^4 - 4866048 z^5 + 131072 z^6) BesselJ[1/4, Sqrt[z]] BesselJ[5/4, Sqrt[z]] + 4 z (15740160975 - 10369012500 z + 2413303200 z^2 - 251254080 z^3 + 14297088 z^4 - 475136 z^5) BesselJ[5/4, Sqrt[z]]^2) Gamma[5/4]^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]