LEADER 02596nam a2200409 i 4500 001 991003627259707536 006 m o d 007 cr cnu|||unuuu 008 190321s2017 sz a o 000 0 eng d 020 $a9783319636306 020 $a9783319636290 024 7 $a10.1007/978-3-319-63630-6$2doi 035 $ab14362399-39ule_inst 082 04$a515.24$223 084 $aLC QA295 084 $aAMS 40-02 100 1 $aCandelpergher, Bernard$0739987 245 10$aRamanujan summation of divergent series$h[e-book] /$cby Bernard Candelpergher 260 $aCham :$bSpringer,$c2017 300 $a1 online resource (xxiii, 195 p.) :$billustrations 336 $atext$btxt$2rdacontent 337 $acomputer$bc$2rdamedia 338 $aonline resource$bcr$2rdacarrier 347 $atext file$bPDF$2rda 490 1 $aLecture notes in mathematics,$x0075-8434 ;$v2185 505 0 $aIntroduction: The Summation of Series --  1 Ramanujan Summation -- 3 Properties of the Ramanujan Summation -- 3 Dependence on a Parameter -- 4 Transformation Formulas -- 5 An Algebraic View on the Summation of Series -- 6 Appendix -- 7 Bibliography -- 8 Chapter VI of the Second Ramanujan's Notebook 520 $aThe aim of this monograph is to give a detailed exposition of the summation method that Ramanujan uses in Chapter VI of his second Notebook. This method, presented by Ramanujan as an application of the Euler-MacLaurin formula, is here extended using a difference equation in a space of analytic functions. This provides simple proofs of theorems on the summation of some divergent series. Several examples and applications are given. For numerical evaluation, a formula in terms of convergent series is provided by the use of Newton interpolation. The relation with other summation processes such as those of Borel and Euler is also studied. Finally, in the last chapter, a purely algebraic theory is developed that unifies all these summation processes. This monograph is aimed at graduate students and researchers who have a basic knowledge of analytic function theory 650 0$aFunctions of complex variables 650 0$aSequences (Mathematics) 650 0$aNumber theory 776 08$iPrinted edition:$z9783319636290 856 40$uhttps://link.springer.com/book/10.1007/978-3-319-63630-6$zAn electronic book accessible through the World Wide Web 907 $a.b14362399$b03-03-22$c21-03-19 912 $a991003627259707536 996 $aRamanujan summation of divergent series$91466442 997 $aUNISALENTO 998 $ale013$b21-03-19$cm$d@ $e-$feng$gsz $h0$i0