Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9372)

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`=-1/2

http://functions.wolfram.com/07.22.03.9372.01

Input Form

HypergeometricPFQ[{-(19/4)}, {-(1/2), 11/4}, z] == ((2 Sqrt[z] (1733106375 + 26143603200 z + 102267360000 z^2 - 207200747520 z^3 + 39321927680 z^4 - 1686110208 z^5 + 16777216 z^6) BesselI[-(1/4), Sqrt[z]]^2 + (-5199319125 + 6162156000 z - 21819283200 z^2 + 185261506560 z^3 - 38296289280 z^4 + 1675624448 z^5 - 16777216 z^6) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] - 2 Sqrt[z] (-5199319125 + 17254036800 z + 63036230400 z^2 - 197998018560 z^3 + 38906953728 z^4 - 1681915904 z^5 + 16777216 z^6) BesselI[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/(61677158400 Sqrt[2] z^(5/4))

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]