Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.ae6e)

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=13/4, b_1`>=-11/2

For fixed z and a₁=13/4, b_1`=-9/2

http://functions.wolfram.com/07.22.03.ae6e.01

Input Form

HypergeometricPFQ[{13/4}, {-(9/2), -(9/4)}, z] == (1/(1913625 Sqrt[2])) (z^(1/4) ((1913625 + 4441500 z + 3823200 z^2 + 2566080 z^3 - 911360 z^4 + 835584 z^5) BesselI[-(1/4), Sqrt[z]]^2 + 4 Sqrt[z] (-1913625 - 2910600 z - 1630800 z^2 - 723840 z^3 + 1089536 z^4 + 32768 z^5) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] + 4 z (1913625 + 1379700 z + 663120 z^2 - 453120 z^3 + 200704 z^4) 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]