Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8396)

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=-23/4, b_1`>=-11/2

For fixed z and a₁=-23/4, b_1`=7/2

http://functions.wolfram.com/07.22.03.8396.01

Input Form

HypergeometricPFQ[{-(23/4)}, {7/2, -(5/4)}, z] == ((4 z (-183635211375 + 916390767600 z + 1679193331200 z^2 + 2734212096000 z^3 - 1423382876160 z^4 + 120340807680 z^5 - 2788163584 z^6 + 16777216 z^7) BesselI[-(1/4), Sqrt[z]]^2 - 4 Sqrt[z] (-550905634125 + 545658913800 z + 1009768636800 z^2 + 1008458035200 z^3 - 676328970240 z^4 + 59313192960 z^5 - 1388838912 z^6 + 8388608 z^7) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] - (1652716902375 - 1322173521900 z + 5036851512000 z^2 + 7927263590400 z^3 + 9682219008000 z^4 - 5577423667200 z^5 + 478601281536 z^6 - 11135877120 z^7 + 67108864 z^8) BesselI[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/(2798105310000 Sqrt[2] z^(7/4))

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]