Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a9e2)

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=-9/4, b_1`>=-11/2

For fixed z and a₁=-9/4, b_1`=-3/2

http://functions.wolfram.com/07.22.03.a9e2.01

Input Form

HypergeometricPFQ[{-(9/4)}, {-(3/2), -(23/4)}, z] == (1/(302841 z^(1/4))) (Sqrt[2] (11 (27531 - 62244 z + 34608 z^2 + 256 z^3) BesselI[1/4, Sqrt[z]]^2 - 12 Sqrt[z] (-100947 + 93632 z + 23584 z^2 + 512 z^3) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] + 44 z (27531 + 11172 z + 1472 z^2) 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]