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

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`=-5/2

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

Input Form

HypergeometricPFQ[{15/4}, {-(5/2), -(23/4)}, -z] == (1/(5246720325 z^(1/4))) (Sqrt[2] ((5246720325 + 9124731000 z + 1216630800 z^2 - 2132000640 z^3 - 539320320 z^4 - 2013462528 z^5 - 781189120 z^6 + 8388608 z^7) BesselJ[1/4, Sqrt[z]]^2 + 4 Sqrt[z] (-5246720325 - 2129103900 z + 2954674800 z^2 - 943810560 z^3 + 1258414080 z^4 - 12582912 z^5 + 74448896 z^6) BesselJ[1/4, Sqrt[z]] BesselJ[5/4, Sqrt[z]] + 4 z (5246720325 - 4866523200 z + 2201522400 z^2 - 1078640640 z^3 + 413122560 z^4 + 141033472 z^5 - 2097152 z^6) 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]