Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.age8)

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`=-9/2

http://functions.wolfram.com/07.22.03.age8.01

Input Form

HypergeometricPFQ[{23/4}, {-(9/2), -(15/4)}, z] == -((1/(215571769875 z^(1/4))) (Sqrt[2] ((-215571769875 + 357689455200 z - 22562971200 z^2 - 81100293120 z^3 - 48977026560 z^4 + 498331975680 z^5 + 640872087552 z^6 + 22867345408 z^7 + 33554432 z^8) BesselI[1/4, Sqrt[z]]^2 + 4 Sqrt[z] (-215571769875 + 70260428700 z + 125865986400 z^2 + 55604767680 z^3 + 808980480 z^4 + 324301455360 z^5 + 78781612032 z^6 + 700448768 z^7) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] + 4 z (-215571769875 - 217168597800 z - 108943758000 z^2 - 47771982720 z^3 - 45302906880 z^4 + 104968028160 z^5 + 5197791232 z^6 + 8388608 z^7) 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]