Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.aa4o)

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=-7/4, b_1`>=-11/2

For fixed z and a₁=-7/4, b_1`=11/2

http://functions.wolfram.com/07.22.03.aa4o.01

Input Form

HypergeometricPFQ[{-(7/4)}, {11/2, 23/4}, z] == (19 (2 Sqrt[z] (126638386875 + 166183617600 z + 68355705600 z^2 + 18785894400 z^3 + 13098352640 z^4 - 1195376640 z^5 + 16777216 z^6) BesselI[-(1/4), Sqrt[z]]^2 - (379915160625 + 263805141600 z + 90810720000 z^2 + 25159680000 z^3 + 12379422720 z^4 - 1184890880 z^5 + 16777216 z^6) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] - 2 Sqrt[z] (230332877775 + 197967369600 z + 76281004800 z^2 + 21624422400 z^3 + 12806062080 z^4 - 1191182336 z^5 + 16777216 z^6) BesselI[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/(225941913600 Sqrt[2] z^(17/4))

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]