Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9148)

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`=-9/2

http://functions.wolfram.com/07.22.03.9148.01

Input Form

HypergeometricPFQ[{-(19/4)}, {-(9/2), -(21/4)}, z] == -((1/(197358525 Sqrt[2])) (z^(1/4) ((-197358525 - 355036500 z - 162470880 z^2 - 2756160 z^3 - 180224 z^4 + 32768 z^5) BesselI[-(1/4), Sqrt[z]]^2 + 4 Sqrt[z] (197358525 + 197149680 z + 18785520 z^2 + 19968 z^3 - 4096 z^4) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] - 4 z (197358525 + 39262860 z + 1409616 z^2 - 43008 z^3 + 8192 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]