Multiple gamma function, its \(q\)- and elliptic analogue.
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Publication:1415048
DOI10.1216/rmjm/1030539697zbMath1042.33003OpenAlexW1997032479MaRDI QIDQ1415048
Publication date: 3 December 2003
Published in: Rocky Mountain Journal of Mathematics (Search for Journal in Brave)
Full work available at URL: http://math.la.asu.edu/~rmmc/rmj/Vol32-2/CONT32-2/CONT32-2.html
Gamma, beta and polygamma functions (33B15) Basic hypergeometric functions in one variable, ({}_rphi_s) (33D15)
Related Items (3)
Multiple Gamma Functions and Their Applications ⋮ Asymptotic formulas for the triple gamma function \(\varGamma _{3}\) by means of its integral representation ⋮ Some two-sided inequalities for multiple Gamma functions and related results
Cites Work
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- Jacobi functions as limit cases of q-ultraspherical polynomials
- The q-analogue of Stirling's formula
- The q-analogue of Hölder's theorem for the gamma function
- Asymptotics of a \(\tau\)-function arising in the two-dimensional Ising model
- Spectral functions, special functions and the Selberg zeta function
- A proof of the classical Kronecker limit formula
- Multiple sine functions and Selberg zeta functions
- Multiple gamma functions and multiple \(q\)-gamma functions
- Asymptotic expansions for \(q\)-gamma, \(q\)-exponential, and \(q\)-Bessel functions
- Determinant formula for solutions of the quantum Knizhnik-Zamolodchikov equation associated with \(U_q (sl_n)\) at \(|q|=1\)
- Summation and transformation formulas for elliptic hypergeometric series.
- On a \(q\)-analogue of the multiple gamma functions
- Spectral transformation chains and some new biorthogonal rational functions
- Gamma factors and Plancherel measures
- Determinants of Laplacians and Multiple Gamma Functions
- Theq-Gamma andq-Beta Functions†
- First order analytic difference equations and integrable quantum systems
- Quantum KZ equation with |q| = 1 and correlation functions of theXXZmodel in the gapless regime
- Commuting difference operators with elliptic coefficients from Baxter's vacuum vectors
- Generalized Lamé functions. I. The elliptic case
- The elliptic gamma function and \(\text{SL}(3,\mathbb Z)\ltimes\mathbb Z^3\).
- On a solution of a \(q\)-difference analogue of Lauricella's \(D\)-type hypergeometric equation with \(|q|=1\)
- The \(q\)-twisted cohomology and the \(q\)-hypergeometric function at \(|q|=1\)
- Generalized Hölder's theorem for Vignéras' multiple gamma function
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