Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8240)

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`=1/2

http://functions.wolfram.com/07.22.03.8240.01

Input Form

HypergeometricPFQ[{-(23/4)}, {1/2, -(17/4)}, z] == -((1/(2076963525 Sqrt[2])) (z^(1/4) ((-2076963525 - 9773946000 z - 7142849280 z^2 - 1888481280 z^3 - 310444032 z^4 - 63963136 z^5 + 4194304 z^6) BesselI[-(1/4), Sqrt[z]]^ 2 + 4 Sqrt[z] (2076963525 + 1116748080 z + 267644160 z^2 + 42921984 z^3 + 7667712 z^4 - 524288 z^5) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] - 512 z (-24763725 - 15187095 z - 3873744 z^2 - 634368 z^3 - 122880 z^4 + 8192 z^5) BesselI[3/4, Sqrt[z]]^2) Gamma[3/4]^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]