Download Metaharmonic lattice point theory by Willi Freeden PDF

By Willi Freeden

Metaharmonic Lattice element concept covers interrelated tools and instruments of spherically orientated geomathematics and periodically mirrored analytic quantity conception. The publication establishes multi-dimensional Euler and Poisson summation formulation such as elliptic operators for the adaptive decision and calculation of formulation and identities of weighted lattice element numbers, particularly the non-uniform Read more...

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Boundary Point Asymptotics . . . . . . . . . . . . . . . . . . . Stationary Point Asymptotics . . . . . . . . . . . . . . . . . . . Abel–Poisson and Gauß–Weierstraß Limits . . . . . . . . . . . . . . . . Gauß–Weierstraß Means . . . . . . . . . . . . . . . . . . . . . Abel–Poisson Means . . . . . . . . . . . . . . . . . . . . . . . 17 18 20 25 28 31 31 32 34 35 35 38 39 42 In this chapter we provide well known one-dimensional tools and methods of basic importance for this work.

17 18 20 25 28 31 31 32 34 35 35 38 39 42 In this chapter we provide well known one-dimensional tools and methods of basic importance for this work. The point of departure is the Gamma function. A central topic is the Stirling formula. Particular attention is paid to generalizations of the Riemann–Lebesgue theorem known from the Fourier theory. 2). 1). 1 Gamma Function and Its Properties First our purpose is to introduce the classical Gamma function. , to N. T. N. N. Lebedev [1973], C.

Radial and Angular Functions . . . . . . . . . . . . . . . . . . . . . . 9 10 11 12 13 14 14 15 Cartesian Nomenclature Throughout this book we base our considerations on the following notational background. The letters N, N0 , Z, R, and C denote the set of positive, non-negative integers, integers, real numbers, and complex numbers, respectively. As usual, we write x, y, . . to represent the elements of the q-dimensional (real) Euclidean space Rq (q ≥ 1).

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