Theory of multivariable Bessel functions and elliptic modular functions
AbstractThe theory of multivariable Bessel functions is exploited to establish further links with the elliptic functions. The starting point of the present investigations is the Fourier expansion of the theta functions, which is used to derive an analogous expansion for the Jacobi functions (sn,dn,cn...) in terms of multivariable Bessel functions, which play the role of Fourier coefficients. An important by product of the analysis is an unexpected link with the elliptic modular functions.
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