Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a8fa)

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=-13/4, b_1`>=-11/2

For fixed z and a₁=-13/4, b_1`=-9/2

http://functions.wolfram.com/07.22.03.a8fa.01

Input Form

HypergeometricPFQ[{-(13/4)}, {-(9/2), 21/4}, z] == -((17 (2 Sqrt[z] (-607225361017275 + 699903224420400 z - 6122718201600 z^2 + 2654179799040 z^3 + 3172719329280 z^4 + 340125548544 z^5 + 14545846272 z^6 + 268435456 z^7) BesselI[1/4, Sqrt[z]]^2 - 3 (-1012042268362125 + 1886179875980400 z + 242867821996800 z^2 + 6047129088000 z^3 + 3493565890560 z^4 + 353249525760 z^5 + 14780727296 z^6 + 268435456 z^7) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] - 2 Sqrt[z] (-3036126805086375 - 818530889576400 z - 30613591008000 z^2 + 5418855936000 z^3 + 3442941296640 z^4 + 351299174400 z^5 + 14747172864 z^6 + 268435456 z^7) BesselI[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/ (87897176801280 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]