Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9120)

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`=-11/2

http://functions.wolfram.com/07.22.03.9120.01

Input Form

HypergeometricPFQ[{-(19/4)}, {-(11/2), -(1/4)}, z] == (1/(5821200 Sqrt[2])) (z^(1/4) (-2 (-2910600 + 4233600 z + 7653345 z^2 + 1516720 z^3 + 118528 z^4 + 4096 z^5) BesselI[-(1/4), Sqrt[z]]^2 + Sqrt[z] (-23284800 + 8848035 z + 1597680 z^2 + 121088 z^3 + 4096 z^4) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] + 2 z (11642400 + 8086365 z + 1547952 z^2 + 119552 z^3 + 4096 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]