Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9556)

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`=7/2

http://functions.wolfram.com/07.22.03.9556.01

Input Form

HypergeometricPFQ[{-(19/4)}, {7/2, 3/4}, z] == ((-4 z (435498525 - 39234358800 z + 117500052600 z^2 - 40598634240 z^3 + 3345039360 z^4 - 81330176 z^5 + 524288 z^6) BesselI[-(1/4), Sqrt[z]]^ 2 + 4 Sqrt[z] (1306495575 - 2986275600 z + 48440114100 z^2 - 19319247360 z^3 + 1647544320 z^4 - 40501248 z^5 + 262144 z^6) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] + (-3919486725 + 8212257900 z - 83615716800 z^2 + 434068437600 z^3 - 159172715520 z^4 + 13299646464 z^5 - 324796416 z^6 + 2097152 z^7) BesselI[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/(152623926000 Sqrt[2] z^(7/4))

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]