Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a97k)

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.a97k.01

Input Form

HypergeometricPFQ[{-(11/4)}, {11/2, -(17/4)}, z] == ((4 z (-39848840868375 - 1951779960900 z - 156992774400 z^2 + 91854233600 z^3 + 15872163840 z^4 + 833617920 z^5 + 16777216 z^6) BesselI[-(1/4), Sqrt[z]]^2 - 4 Sqrt[z] (-119546522605125 - 28626106093200 z - 403384212000 z^2 + 51684864000 z^3 + 8210677760 z^4 + 422051840 z^5 + 8388608 z^6) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] - (358639567815375 + 154190616911100 z + 14019236708400 z^2 - 503927424000 z^3 + 384715161600 z^4 + 64348487680 z^5 + 3351248896 z^6 + 67108864 z^7) BesselI[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/(135973344000 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]