An addition formula for the Jacobian theta function and its applications

Liu, Zhiguo

doi:10.1016/j.aim.2006.10.005

Cited by 32 publications

(13 citation statements)

References 16 publications

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“…We note that Theorem 1, Theorem 2, and Theorem 3 below are consequences of the following result which is an extension of a theorem of Liu [8,Theorem 1].…”

Section: A General Resultsmentioning

confidence: 92%

Proving some identities of Gosper on $q$-trigonometric functions

Bachraoui

2019

Proc. Amer. Math. Soc.

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“…We note that Theorem 1, Theorem 2, and Theorem 3 below are consequences of the following result which is an extension of a theorem of Liu [8,Theorem 1].…”

Section: A General Resultsmentioning

confidence: 92%

Proving some identities of Gosper on $q$-trigonometric functions

Bachraoui

2019

Proc. Amer. Math. Soc.

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“…The derivatives of Jacobi theta functions as eigenfunctions of the DFT first appeared in Ref. 6 another addition formula for theta function is given which, in particular, implies the Winquist identity as well as other identities. The properties of Jacobi theta functions and their derivatives under DFT are further investigated in Ref.…”

Section: Introductionmentioning

confidence: 93%

Discrete Fourier transform and Jacobi θ function identities

Malekar

Bhate

2010

Journal of Mathematical Physics

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Erratum: Analysis of the numerically implemented angular spectrum approach based on the evaluation of twodimensional acoustic fields. Part I. Errors due to the discrete Fourier transform and discretization [J. Acoust. Soc.Classical theta function identities are derived using properties of eigenvectors corresponding to the discrete Fourier transform ⌽͑2͒. In particular, an extended Watson addition formula is obtained corresponding to ⌽͑2͒, and the corresponding result for the discrete Fourier transform ⌽͑3͒ is obtained.

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“…Corollary 1.1 is also proved in Section 3. In Section 4, we use Theorem 1.2 to derive the following new addition formula for theta functions of degree 5 which is obviously different from the addition formula in [7], and some applications are given. In particular, this addition formula allows us to give an extension of the Hirschhorn septuple product identities.…”

Section: Theorem 13 Suppose That F (Z) Is An Even Entire Function Omentioning

confidence: 99%