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

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`=-11/2

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

Input Form

HypergeometricPFQ[{23/4}, {-(11/2), 17/4}, z] == (13 (18 Sqrt[z] (133075906425 - 101391166800 z - 46235481600 z^2 - 13483008000 z^3 - 2334720000 z^4 + 196083712 z^5 + 4194304 z^6) BesselI[1/4, Sqrt[z]]^2 + (-5988415789125 + 8821031511600 z + 5337754329600 z^2 + 1415715840000 z^3 + 317988864000 z^4 - 1651507200 z^5 - 2617245696 z^6 + 67108864 z^7) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] + 6 Sqrt[z] (-1996138596375 - 1318085168400 z - 383760115200 z^2 - 84225024000 z^3 - 6070272000 z^4 + 917504000 z^5 + 4194304 z^6) BesselI[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/ (249165987840 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]