Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8610)

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=-21/4, b_1`>=-11/2

For fixed z and a₁=-21/4, b_1`=-9/2

http://functions.wolfram.com/07.22.03.8610.01

Input Form

HypergeometricPFQ[{-(21/4)}, {-(9/2), 17/4}, z] == ((-2 Sqrt[z] (2382191800913925 - 3278715596956800 z - 37164776140800 z^2 + 619411658342400 z^3 + 141702414336000 z^4 + 14475658788864 z^5 + 921673138176 z^6 + 45097156608 z^7 + 4294967296 z^8) BesselI[1/4, Sqrt[z]]^2 + 3 (3970319668189875 - 8287864425640800 z + 1133383169318400 z^2 + 780275723673600 z^3 + 156333735936000 z^4 + 15376853237760 z^5 + 967474937856 z^6 + 48855252992 z^7 + 4294967296 z^8) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] + 2 Sqrt[z] (11910959004569625 + 546452599492800 z + 693908062848000 z^2 + 745474893004800 z^3 + 153705981542400 z^4 + 15224253972480 z^5 + 959723864064 z^6 + 48318382080 z^7 + 4294967296 z^8) BesselI[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/(933907503513600 Sqrt[2] z^(11/4))

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]