Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.aa3s)

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=-7/4, b_1`>=-11/2

For fixed z and a₁=-7/4, b_1`=11/2

http://functions.wolfram.com/07.22.03.aa3s.01

Input Form

HypergeometricPFQ[{-(7/4)}, {11/2, -(9/4)}, z] == (1/(63648000 Sqrt[2] z^(15/4))) ((4 z (-10016466075 - 211988700 z - 61286400 z^2 + 40888320 z^3 + 8519680 z^4 + 524288 z^5) BesselI[-(1/4), Sqrt[z]]^2 - 4 Sqrt[z] (-30049398225 - 6359661000 z - 7660800 z^2 + 23546880 z^3 + 4423680 z^4 + 262144 z^5) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] - (90148194675 + 36250067700 z + 2765070000 z^2 - 187084800 z^3 + 172892160 z^4 + 34603008 z^5 + 2097152 z^6) 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]