Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a90k)

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

For fixed z and a₁=-11/4, b_1`=-1/2

http://functions.wolfram.com/07.22.03.a90k.01

Input Form

HypergeometricPFQ[{-(11/4)}, {-(1/2), 19/4}, z] == (1/(817889280 Sqrt[2] z^(13/4))) ((2 Sqrt[z] (884458575 + 518918400 z - 103783680 z^2 + 368476160 z^3 + 506265600 z^4 - 377487360 z^5 + 16777216 z^6) BesselI[-(1/4), Sqrt[z]]^2 - (2653375725 + 5599994400 z - 795674880 z^2 + 246005760 z^3 + 298516480 z^4 - 367001600 z^5 + 16777216 z^6) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] - 2 Sqrt[z] (-2653375725 + 60540480 z - 196035840 z^2 + 378470400 z^3 + 418447360 z^4 - 373293056 z^5 + 16777216 z^6) 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]