Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.adb6)

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=9/4, b_1`>=-11/2

For fixed z and a₁=9/4, b_1`=-9/2

http://functions.wolfram.com/07.22.03.adb6.01

Input Form

HypergeometricPFQ[{9/4}, {-(9/2), 19/4}, z] == -((1/(31457280 Sqrt[2] z^(13/4))) (11 (-10 Sqrt[z] (25649298675 + 27617662800 z + 4491002880 z^2 + 248479744 z^3 + 3932160 z^4) BesselI[-(1/4), Sqrt[z]]^2 + (384739480125 + 1000534626000 z + 284430182400 z^2 + 25472778240 z^3 + 781189120 z^4 + 4194304 z^5) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] - 14 Sqrt[z] (54962782875 + 25679581200 z + 3717043200 z^2 + 192184320 z^3 + 2883584 z^4) 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]