Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a96d)

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

For fixed z and a₁=-11/4, b_1`=9/2

http://functions.wolfram.com/07.22.03.a96d.01

Input Form

HypergeometricPFQ[{-(11/4)}, {9/2, -(13/4)}, -z] == ((4 z (15740160975 + 1332500400 z + 1099699200 z^2 - 306032640 z^3 + 26869760 z^4 - 1048576 z^5) BesselJ[-(1/4), Sqrt[z]]^2 + 4 Sqrt[z] (-47220482925 + 4996876500 z - 674150400 z^2 + 162293760 z^3 - 13762560 z^4 + 524288 z^5) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] + (141661448775 - 41973762600 z + 3476088000 z^2 + 4754534400 z^3 - 1252638720 z^4 + 108527616 z^5 - 4194304 z^6) BesselJ[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/(1861704000 Sqrt[2] z^(11/4))

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]