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

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=23/4, b_1`>=-11/2

For fixed z and a₁=23/4, b_1`=1/2

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

Input Form

HypergeometricPFQ[{23/4}, {1/2, -(19/4)}, z] == -((1/(4334247225 z^(1/4))) (Sqrt[2] ((-4334247225 + 19161935100 z - 30172443840 z^2 + 15260571648 z^3 - 2599059456 z^4 + 919339008 z^5 + 4194304 z^6) BesselI[1/4, Sqrt[z]]^2 + 12 Sqrt[z] (-1444749075 + 4460979600 z - 1527160320 z^2 - 835559424 z^3 + 276627456 z^4 + 17825792 z^5) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] + 4 z (-4334247225 - 703911600 z + 4833400320 z^2 - 1133862912 z^3 + 190513152 z^4 + 1048576 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]