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

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`=-11/2

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

Input Form

HypergeometricPFQ[{21/4}, {-(11/2), -(17/4)}, -z] == -((1/(1028096944875 Sqrt[2])) (z^(1/4) ((-1028096944875 + 2287103364000 z - 1744874913600 z^2 + 604146816000 z^3 - 165418606080 z^4 + 102651494400 z^5 + 250013286400 z^6 - 17901289472 z^7 + 33554432 z^8) BesselJ[-(1/4), Sqrt[z]]^2 + 4 Sqrt[z] (-1028096944875 + 1464625808100 z - 646283383200 z^2 + 182273232960 z^3 - 53892034560 z^4 + 15739944960 z^5 - 51535413248 z^6 + 641728512 z^7) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] - 4 z (1028096944875 - 642148252200 z + 205673897520 z^2 - 54399945600 z^3 + 20530298880 z^4 + 50641305600 z^5 - 4316987392 z^6 + 8388608 z^7) 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]