Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.afh0)

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=19/4, b_1`>=-11/2

For fixed z and a₁=19/4, b_1`=-11/2

http://functions.wolfram.com/07.22.03.afh0.01

Input Form

HypergeometricPFQ[{19/4}, {-(11/2), -(11/4)}, z] == -((1/(8320313925 z^(1/4))) (Sqrt[2] (3 (-2773437975 + 4675878900 z - 424947600 z^2 - 1097712000 z^3 + 781482240 z^4 - 1948348416 z^5 + 1534787584 z^6 + 40894464 z^7) BesselI[1/4, Sqrt[z]]^2 + 4 Sqrt[z] (-8320313925 + 2933884800 z + 4750099200 z^2 + 1782950400 z^3 + 2212600320 z^4 + 662003712 z^5 + 563478528 z^6 + 2097152 z^7) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] + 12 z (-2773437975 - 2719955700 z - 1338876000 z^2 - 670824000 z^3 - 478786560 z^4 + 250036224 z^5 + 9699328 z^6) BesselI[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]