<p>Disertacija se bavi sumiranjem redova sa specijalnim funkcijama. Ovi redovi se posredstvom trigonometrijskih redova svode na redove sa Riemannovom zeta funkci­jom i srodnim funkcijama. U određenim slučajevima sumacione formule se mogu dovesti na takozvani zatvoreni oblik, što znači da se beskonačni redovi predstavljaju konačnim sumama. Predloženi metodi sumacije omogućavaju ubrzanje konvergencije, a mogu se primeniti i kod nekih graničnih problema matematičke fizike. Sumacione formule uključuju kao specijalne slučajeve neke formule poznate iz literature, ali i nove sume, s obzirom da su opšteg karaktera. Pomoću ovih formula sumirani su i redovi sa integralima trigonometrijskih i specijalnih funkcija.</p> / <p>This dissertation deals with the summation of series over special functions. Through<br />trigonometric series these series are reduced to series in terms of Riemann zeta and<br />related functions. They can be brought in closed form in some cases, i.e. infinite<br />series are expressed as finite sums. Closed form formulas make it possible to accele­<br />rate the convergence of some series, and have many applications in various scientific<br />fields as well. For example, closed form solutions of the boundary value problem in<br />mathematical physics can be obtained. Summation formulas include particular cases<br />known from the literature, but because of their general character one can come to<br />new sums. By means of these formuláis the sums of series over integrals containing<br />trigonometric or special functions have been found.</p>
Identifer | oai:union.ndltd.org:uns.ac.rs/oai:CRISUNS:(BISIS)73367 |
Date | 11 July 2003 |
Creators | Vidanović Mirjana |
Contributors | Pilipović Stevan, Perišić Dušanka, Stanković Miomir, Tričković Slobodan |
Publisher | Univerzitet u Novom Sadu, Prirodno-matematički fakultet u Novom Sadu, University of Novi Sad, Faculty of Sciences at Novi Sad |
Source Sets | University of Novi Sad |
Language | Serbian |
Detected Language | English |
Type | PhD thesis |
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