Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.aa3d)

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=-7/4, b_1`>=-11/2

For fixed z and a₁=-7/4, b_1`=9/2

http://functions.wolfram.com/07.22.03.aa3d.01

Input Form

HypergeometricPFQ[{-(7/4)}, {9/2, 23/4}, -z] == (19 (2 Sqrt[z] (-5065535475 - 29331862560 z + 23709853440 z^2 - 9513713664 z^3 + 8935636992 z^4 + 1004535808 z^5 + 16777216 z^6) BesselJ[-(1/4), Sqrt[z]]^2 + (15196606425 + 64838854080 z - 35597802240 z^2 + 13606354944 z^3 - 8335982592 z^4 - 994050048 z^5 - 16777216 z^6) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] + 2 Sqrt[z] (15196606425 - 42226984800 z + 28042350336 z^2 - 11386109952 z^3 + 8691056640 z^4 + 1000341504 z^5 + 16777216 z^6) BesselJ[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/(162678177792 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]