Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9488)

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=-19/4, b_1`>=-11/2

For fixed z and a₁=-19/4, b_1`=5/2

http://functions.wolfram.com/07.22.03.9488.01

Input Form

HypergeometricPFQ[{-(19/4)}, {5/2, -(17/4)}, z] == ((8 z (14192219475 + 10719651600 z + 2198419200 z^2 + 227184640 z^3 + 15400960 z^4 + 1048576 z^5) BesselI[-(1/4), Sqrt[z]]^2 - 4 Sqrt[z] (33229228725 + 12818106000 z + 2378476800 z^2 + 238571520 z^3 + 16056320 z^4 + 1048576 z^5) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] - (-99687686175 + 150253903800 z + 91247184000 z^2 + 18105292800 z^3 + 1851555840 z^4 + 125304832 z^5 + 8388608 z^6) BesselI[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/ (69232117500 Sqrt[2] z^(3/4))

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]