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

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`=-11/2

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

Input Form

HypergeometricPFQ[{11/4}, {-(11/2), 21/4}, z] == (221 (-6 Sqrt[z] (-22489828185825 + 21055565638800 z + 5191227740160 z^2 + 409773686784 z^3 + 13061586944 z^4 + 130023424 z^5) BesselI[1/4, Sqrt[z]]^2 + (-337347422787375 + 555724985230800 z + 214138144281600 z^2 + 24114090147840 z^3 + 1117360226304 z^4 + 20107493376 z^5 + 67108864 z^6) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] - 18 Sqrt[z] (37483046976375 + 18216612968400 z + 2884015411200 z^2 + 187193180160 z^3 + 5226627072 z^4 + 46137344 z^5) BesselI[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/(20346568704 Sqrt[2] z^(15/4))

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]