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Some Remarks on Glaisher-Ramanujan Type Integrals

Patkowski A. E., Wolf M.

Computational Methods in Science and Technology

2016

Vol. 22, No. 2

103--108

Some integrals of the Glaisher-Ramanujan type are established in a more general form than in previous studies. As an application we prove some Ramanujan-type series identities, as well as a new formula for the Dirichlet beta function at the value s = 3. We also present a Mathematica program calculating values of beta function at odd positive arguments.

Trigonometric Series and Set Theory

Kechris A. S.

Wiadomości Matematyczne

2012

T. 48, Nr 2

109--118

The historical survey concerning the interactions between the theory of trigonometric series and descriptive set theory. We concentrate here on the area related to problems of uniqueness for trigonometric series. Detailed historical and bibliographical references can be found in the books and survey papers listed at the end.

Integrability of trigonometric series with generalized semi-convex coefficients

Krasniqi X. Z.

Opuscula Mathematica

2012

Vol. 32, no. 3

521-528

In this paper we deal with cosine and sine trigonometric series with generalized semi-convex coefficients. Integrability conditions for them are obtained.

Integrability of Double Cosine Trigonometric Series with coefficients of bounded variation of second order

Krasniqi X. Z.

Commentationes Mathematicae

2011

Vol. 51, [Z] 2

125-139

In this paper integrability condition for double cosine trigonometric series with coefficients of bounded variation of second order has been obtained. This condition is given explicitly in terms of the coefficients. The result extends a previous result of Telyakovskii from one dimensional case to two dimensional case