Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8333)

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=-23/4, b_1`>=-11/2

For fixed z and a₁=-23/4, b_1`=5/2

http://functions.wolfram.com/07.22.03.8333.01

Input Form

HypergeometricPFQ[{-(23/4)}, {5/2, -(21/4)}, -z] == ((8 z (8709520117725 - 6444151585200 z + 1284392044800 z^2 - 126442352640 z^3 + 7728332800 z^4 - 347078656 z^5 + 16777216 z^6) BesselJ[-(1/4), Sqrt[z]]^2 - 4 Sqrt[z] (20635351038225 - 7660926075600 z + 1383056236800 z^2 - 132050718720 z^3 + 7973437440 z^4 - 357564416 z^5 + 16777216 z^6) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] + (61906053114675 + 91712671281000 z - 54726931324800 z^2 + 10559785420800 z^3 - 1028327178240 z^4 + 62573248512 z^5 - 2810183680 z^6 + 134217728 z^7) BesselJ[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/(42162359557500 Sqrt[2] z^(3/4))

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]