Results 31 to 40 of about 2,378 (305)
Dualizing the Poisson summation formula.
Proceedings of the National Academy of Sciences, 1991 If f(x) and g(x) are a Fourier cosine transform pair, then the Poisson summation formula can be written as 2sumfrominfinityn = 1g(n) + g(0) = 2sumfrominfinityn = 1f(n) + f(0). The concepts of linear transformation theory lead to the following dual of this classical relation. Let phi(x) and gamma(x) = phi(1/x)/x have absolutely convergent integrals over
Duffin, Richard J., Weinberger, Hans F.
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Poisson Summation Formulae Associated with the Special Affine Fourier Transform and Offset Hilbert Transform [PDF]
, 2017 This paper investigates the generalized pattern of Poisson summation formulae from the special affine Fourier transform (SAFT) and offset Hilbert transform (OHT) points of view. Several novel summation formulae are derived accordingly.
Zhi-Hai Zhuo
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Summation formulae involving the Laguerre polynomial
, 1998 A general result involving the generalized hypergeometric function is deduced by the elementary manipulation of series. Kummer's first theorem for the confluent hypergeometric function and two summation formulae for the Gauss hypergeometric function are ...
Exton, H.
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Partial Sums of Two Quartic q-Series
Symmetry, Integrability and Geometry: Methods and Applications, 2009 The partial sums of two quartic basic hypergeometric series are investigated by means of the modified Abel lemma on summation by parts. Several summation and transformation formulae are consequently established.
Wenchang Chu, Chenying Wang
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A proof of new summation formulae by using sampling theorems
, 1993 Using symbolic manipulation programs, William Gosper has obtained in the last two years new, but unusual, summation formulae involving trigonometric functions.
Zayed, Ahmed I., Ahmed I. Zayed
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Mathematical and Computer Modelling of Dynamical SystemsThis study introduces a new approach to the development of generalized 1-parameter, 2-variable Hermite–Frobenius–Euler polynomials, which are characterized by their generating functions, series definitions and summation formulae.
Mohra Zayed +3 more
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A New Old Babylonian Date List with Hammurapi Year Names
Dirāsāt fī al-tārīẖ wa-al-āṯār, 2023 This paper contains the publication of a previously unknown date list of Hammurapi, the king of Babylon, with his year formulae, kept in the Sulaymaniyah Museum in Iraq. The tablet originally contained the year formulae for 42 years of Hammurapi's reign
Ardalan Khwshnaw
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Why does the sign problem occur in evaluating the overlap of HFB wave functions?
Physics Letters B, 2018 For the overlap matrix element between Hartree–Fock–Bogoliubov states, there are two analytically different formulae: one with the square root of the determinant (the Onishi formula) and the other with the Pfaffian (Robledo's Pfaffian formula).
Takahiro Mizusaki +2 more
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On the Mean Values of Certain Character Sums
Abstract and Applied Analysis, 2013 Let q≥5 be an odd number. In this paper, we study the fourth power mean of certain character sums ∑χmodq,χ-1=-1*∑1≤a≤q/4aχa4 and ∑χmodq,χ-1=1*∑1≤a≤q/4aχa4, where ∑* denotes the summation over primitive characters modulo q, and give some asymptotic ...
Zhefeng Xu, Huaning Liu
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A Generalized Poisson Summation Formula
Applied and Computational Harmonic Analysis, 1996 The authors give two proofs for a generalization of the Poisson formula \(\sum_{n\in Z} f(n) = \sum_{n\in Z} \widehat f(n)\). Although the generalization involves abelian groups only, the original proofs went by the way of the Heisenberg group and its discrete subgroups.
Auslander, Louis, Meyer, Yves
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