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

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=21/4, b_1`>=-11/2

For fixed z and a₁=21/4, b_1`=-9/2

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

Input Form

HypergeometricPFQ[{21/4}, {-(9/2), 11/4}, z] == (1/(114566400 Sqrt[2] z^(5/4))) ((2 Sqrt[z] (78316875 + 205264800 z + 76377600 z^2 - 37539840 z^3 + 1515520 z^4 - 131072 z^5) BesselI[-(1/4), Sqrt[z]]^2 - (234950625 + 801964800 z + 840153600 z^2 - 153354240 z^3 - 42024960 z^4 + 4456448 z^5) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] + 2 Sqrt[z] (234950625 + 300736800 z + 45826560 z^2 - 42117120 z^3 + 2039808 z^4 - 131072 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]