Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a8tw)

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.a8tw.01

Input Form

HypergeometricPFQ[{-(11/4)}, {-(11/2), 19/4}, z] == ((2 Sqrt[z] (14235360764625 + 12631446828000 z + 85275590400 z^2 + 162041118720 z^3 + 25528565760 z^4 + 1121976320 z^5 + 16777216 z^6) BesselI[-(1/4), Sqrt[z]]^2 - (42706082293875 + 102970275408000 z + 12023858246400 z^2 + 250925875200 z^3 + 26257981440 z^4 + 1132462080 z^5 + 16777216 z^6) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] - 2 Sqrt[z] (-42706082293875 - 11863966514400 z - 596929132800 z^2 + 168892416000 z^3 + 25815613440 z^4 + 1126170624 z^5 + 16777216 z^6) BesselI[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/ (235552112640 Sqrt[2] z^(13/4))

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]