Abstract
We prove a formula expressing a generaln byn Toeplitz determinant as a Fredholm determinant of an operator 1 −K acting onl 2 (n,n+1,...), where the kernelK admits an integral representation in terms of the symbol of the original Toeplitz matrix. The proof is based on the results of one of the authors, see [14], and a formula due to Gessel which expands any Toeplitz determinant into a series of Schur functions. We also consider 3 examples where the kernel involves the Gauss hypergeometric function and its degenerations.
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Borodin, A., Okounkov, A. A Fredholm determinant formula for Toeplitz determinants. Integr equ oper theory 37, 386–396 (2000). https://doi.org/10.1007/BF01192827
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DOI: https://doi.org/10.1007/BF01192827