O zastosowaniu sumowania według Eisensteina do pewnej sumy podwójnej

• Authors: Agata Matczyk , Vladimir Mityushev , Zbigniew Powązka

Abstracts

PL

The lattice sum S_2 for the square array conditionally converges. Having used physical arguments, Rayleigh chose an order of summation in such a way that S_2 = π. The Eisenstein summation method applied to S2 yields the same result. This paper is devoted to a rigorous proof of S_2 = π for the Eisenstein summation method. The study can be used in class for students as an interesting example which illustrates different types of convergence.

• Publisher: Uniwersytet Komisji Edukacji Narodowej w Krakowie
• Journal: Annales Universitatis Paedagogicae Cracoviensis. Studia ad Didacticam Mathematicae Pertinentia
• Year: 2009
• Volume: 2
• Pages: 153-157

Dates

published

2009

Contributors

author

Agata Matczyk

author

Vladimir Mityushev

• Instytut Matematyki Uniwersytet Pedagogiczny Kraków

author

Zbigniew Powązka

• Instytut Matematyki Uniwersytet Pedagogiczny Kraków

Identifiers

Biblioteka Nauki

1789303