Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9376)

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`=-1/2

http://functions.wolfram.com/07.22.03.9376.01

Input Form

HypergeometricPFQ[{-(19/4)}, {-(1/2), 15/4}, z] == ((2 Sqrt[z] (-157712680125 + 27729702000 z + 1143500716800 z^2 + 3340810137600 z^3 - 5498324582400 z^4 + 857069322240 z^5 - 31121735680 z^6 + 268435456 z^7) BesselI[-(1/4), Sqrt[z]]^2 + (473138040375 + 637783146000 z - 29578348800 z^2 - 1023819264000 z^3 + 5011808256000 z^4 - 838069125120 z^5 + 30953963520 z^6 - 268435456 z^7) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] - 2 Sqrt[z] (473138040375 - 371578006800 z + 916928812800 z^2 + 2248736256000 z^3 - 5295720038400 z^4 + 849393745920 z^5 - 31054626816 z^6 + 268435456 z^7) BesselI[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/ (2691366912000 Sqrt[2] z^(9/4))

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]