Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a8pe)

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`=7/2

http://functions.wolfram.com/07.22.03.a8pe.01

Input Form

HypergeometricPFQ[{-(13/4)}, {7/2, 1/4}, z] == (1/(3028410 Sqrt[2] z^(5/4))) ((16 z (366705 - 2145600 z + 1658064 z^2 - 194048 z^3 + 4096 z^4) BesselI[1/4, Sqrt[z]]^2 - 12 Sqrt[z] (-78975 - 1908960 z + 2988640 z^2 - 380928 z^3 + 8192 z^4) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] + (-1184625 + 1544400 z + 17291520 z^2 - 24264960 z^3 + 3055616 z^4 - 65536 z^5) 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]