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

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=5/4, b_1`>=-11/2

For fixed z and a₁=5/4, b_1`=-11/2

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

Input Form

HypergeometricPFQ[{5/4}, {-(11/2), 23/4}, z] == (1/(805306368 Sqrt[2] z^(17/4))) (19 (2 Sqrt[z] (83378541621375 + 87697569445200 z + 12486782880000 z^2 + 573721374720 z^3 + 7991197696 z^4 + 16777216 z^5) BesselI[-(1/4), Sqrt[z]]^2 - 5 (50027124972825 + 128850351149520 z + 33815426261760 z^2 + 2584463192064 z^3 + 65509785600 z^4 + 419430400 z^5) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] + 2 Sqrt[z] (250135624864125 + 110629089370800 z + 14382337432320 z^2 + 613643489280 z^3 + 8257536000 z^4 + 16777216 z^5) 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]