Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8288)

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`=3/2

http://functions.wolfram.com/07.22.03.8288.01

Input Form

HypergeometricPFQ[{-(23/4)}, {3/2, -(17/4)}, z] == -((1/(51924088125 Sqrt[2])) (z^(1/4) ((-51924088125 - 106376029200 z - 40413139200 z^2 - 7319654400 z^3 - 917831680 z^4 - 152043520 z^5 + 8388608 z^6) BesselI[-(1/4), Sqrt[z]]^2 - 32 Sqrt[z] (-2336857425 - 734202000 z - 125798400 z^2 - 15605760 z^3 - 2293760 z^4 + 131072 z^5) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] + (99687686175 + 121098121200 z + 42725088000 z^2 + 7593062400 z^3 + 952565760 z^4 + 149946368 z^5 - 8388608 z^6) BesselI[3/4, Sqrt[z]]^2) Gamma[3/4]^2))

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]