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

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

For fixed z and a₁=11/4, b_1`=-9/2

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

Input Form

HypergeometricPFQ[{11/4}, {-(9/2), -(7/4)}, z] == -((1/(416745 z^(1/4))) (Sqrt[2] (9 (-46305 + 76440 z - 10080 z^2 + 26880 z^3 - 64512 z^4 + 32768 z^5) BesselI[1/4, Sqrt[z]]^2 + 4 Sqrt[z] (-416745 + 132300 z + 191520 z^2 + 262080 z^3 + 116736 z^4 + 16384 z^5) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] + 60 z (-27783 - 28224 z - 17808 z^2 - 12544 z^3 + 4096 z^4) 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]