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Discrete Fourier Transform and Theta Function Identities

In: Current Trends in Mathematical Analysis and Its Interdisciplinary Applications

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  • R. A. Malekar

    (National Defence Academy, Department of Mathematics)

Abstract

The classical identities of the Jacobi theta functions are obtained from the multiplicities of the eigenvalues i k and the corresponding eigenvectors of the DFT Φ(n) expressed in terms of the theta functions. An extended version of the classical Watson addition formula and Riemann’s identity on theta functions is derived. Watson addition formula and Riemann’s identity are obtained as a particular case. An extensions of some classical identities corresponding to the theta functions θ a,b(x, τ) with a,b ∈ 1 3 ℤ $$\frac {1}{3}\mathbb {Z}$$ are also derived.

Suggested Citation

  • R. A. Malekar, 2019. "Discrete Fourier Transform and Theta Function Identities," Springer Books, in: Hemen Dutta & Ljubiša D. R. Kočinac & Hari M. Srivastava (ed.), Current Trends in Mathematical Analysis and Its Interdisciplinary Applications, chapter 0, pages 55-99, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-15242-0_2
    DOI: 10.1007/978-3-030-15242-0_2
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