Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9336)

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`=-3/2

http://functions.wolfram.com/07.22.03.9336.01

Input Form

HypergeometricPFQ[{-(19/4)}, {-(3/2), 23/4}, z] == -(((2 Sqrt[z] (17865510428390625 + 13176239310234000 z - 1689515283456000 z^2 + 353993678438400 z^3 - 683857487462400 z^4 - 493814336716800 z^5 - 259306637230080 z^6 + 140074989649920 z^7 - 6987911790592 z^8 + 68719476736 z^9) BesselI[-(1/4), Sqrt[z]]^2 + (-53596531285171875 - 121199622746202000 z + 2534272925184000 z^2 - 1641243418214400 z^3 + 653526790963200 z^4 + 491164375449600 z^5 + 182697842442240 z^6 - 135822972026880 z^7 + 6944962117632 z^8 - 68719476736 z^9) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] + 2 Sqrt[z] (53596531285171875 + 6860356004502000 z + 253427292518400 z^2 - 438160007577600 z^3 + 758370661171200 z^4 + 515506647859200 z^5 + 226891042652160 z^6 - 138354855247872 z^7 + 6970731921408 z^8 - 68719476736 z^9) BesselI[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/(1441578929356800 Sqrt[2] z^(17/4)))

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]