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Lattice Sums for Double Periodic Polyanalytic Functions by Piotr Drygaś; Vladimir Mityushev is a Mathematics article available to read on EtoBox.
What is Lattice Sums for Double Periodic Polyanalytic Functions about?
## Abstract In 1892, Lord Rayleigh estimated the effective conductivity of rectangular arrays of disks and proved, employing the Eisenstein summation, that the lattice sum $$S\_2$$ S 2 is equal to $$\pi $$ π for the square array. Further, it became clear that such equality can be treated as a necessary condition of the macroscopic isotropy of composites governed by the Laplace equation. This yielded the description of two-dimensional conducting composites by the classic elliptic functions, including the conditionally convergent Eisenstein series. In 1935, Natanzon used a polyharmonic function to solve the plane elasticity problem. This paper is devoted to the extension of the classic lattice sums to the lattice sums for double periodic (pseudoperiodic) polyanalytic functions. The exact relations and computationally effective formulae between the polyanalytic and classic lattice sums are established. Polynomial representations of the lattice sums are obtained. They are a source of new exact formulae for the lattice sums.
Who reads Lattice Sums for Double Periodic Polyanalytic Functions?
It is typically read by researchers, students, and practitioners in Mathematics.
- Author
- Piotr Drygaś; Vladimir Mityushev
- Publisher
- Springer Science and Business Media LLC
- Published
- 2023
- Language
- EN
- Field
- Mathematics (Physical Sciences)