Results 31 to 40 of about 58,299 (310)
Poisson summation formula [PDF]
, 1998 The Poisson summation (PS) formula describes the fundamental duality between periodization and decimation operators under the Fourier transform. In this chapter, the finite abelian group version of the PS formula is derived as a simple application of the character formulas of Chapter 3. The general case is equally simple to prove, but special care must
Richard Tolimieri, Myoung An
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Evaluation of Infinite Series by Integrals
Mathematics, 2022 We examine a large class of infinite triple series and establish a general summation formula. This is done by expressing the triple series in terms of definite integrals involving arctangent function that are evaluated in turn in closed forms.
Chunli Li, Wenchang Chu
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A dimensionally continued Poisson summation formula
, 2011 We generalize the standard Poisson summation formula for lattices so that it operates on the level of theta series, allowing us to introduce noninteger dimension parameters (using the dimensionally continued Fourier transform).
A. Córdoba +39 more
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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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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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A simple proof of Bailey's very-well-poised 6-psi-6 summation
, 2000 We give elementary derivations of some classical summation formulae for bilateral (basic) hypergeometric series. In particular, we apply Gauss' 2-F-1 summation and elementary series manipulations to give a simple proof of Dougall's 2-H-2 summation ...
Schlosser, M.
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A Poisson “Half-Summation” Formula
Annals of Mathematics and Physics, 2022 A generalization of Poisson’s summation formula is derived – in a non-rigorous way – allowing evaluation of sums from 1 (or any finite integer) ∞ instead of the usual range -∞+∞. This is achieved in two ways, either by introducing a converging factor in a geometric series of exponential functions and letting it approach zero in a controlled way or by ...
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Explicit formulae for Bernoulli numbers
AIMS MathematicsBy examining the connection coefficients, we systematically review and extend (with an extra integer parameter) several double sum expressions for the Bernoulli numbers. New summation formulae are also established explicitly.
Nadia N. Li , Wenchang Chu
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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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