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010   $a9783319636306
010   $a3-319-63630-8
024 7 $a10.1007/978-3-319-63630-6
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035   $a(DE-He213)978-3-319-63630-6
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035   $a(OCoLC)1004663268
035   $a(PPN)204533260
035   $a(EXLCZ)994100000000587416
100   $a20170912d2017      u|         0
101 0 $aeng
135   $aurnn#008mamaa
181   $ctxt$2rdacontent
182   $cc$2rdamedia
183   $acr$2rdacarrier
200 10$aRamanujan summation of divergent series /$fby Bernard Candelpergher
205   $a1st ed. 2017.
210  1$aCham :$cSpringer International Publishing, AG$d2017.
215   $a1 online resource (XXIII, 195 p. 7 illus.)
225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v2185
311 1 $a9783319636290 
311 1 $a3-319-63629-4 
327   $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.
330   $aThe aim of this monograph is to give a detailed exposition of the summation method that Ramanujan uses in Chapter VI of his second Notebook. This method, presented by Ramanujan as an application of the Euler-MacLaurin formula, is here extended using a difference equation in a space of analytic functions. This provides simple proofs of theorems on the summation of some divergent series. Several examples and applications are given. For numerical evaluation, a formula in terms of convergent series is provided by the use of Newton interpolation. The relation with other summation processes such as those of Borel and Euler is also studied. Finally, in the last chapter, a purely algebraic theory is developed that unifies all these summation processes. This monograph is aimed at graduate students and researchers who have a basic knowledge of analytic function theory.
410  0$aLecture Notes in Mathematics,$x0075-8434 ;$v2185
606   $aSequences (Mathematics)
606   $aFunctions of complex variables
606   $aNumber theory
606   $aSuccessions (Matemātica)$2lemac
606   $aNombres, Teoria de$2lemac
606   $aFuncions de variables complexes$2lemac
606   $aSequences, Series, Summability$3https://scigraph.springernature.com/ontologies/product-market-codes/M1218X
606   $aFunctions of a Complex Variable$3https://scigraph.springernature.com/ontologies/product-market-codes/M12074
606   $aNumber Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M25001
615  0$aSequences (Mathematics)
615  0$aFunctions of complex variables.
615  0$aNumber theory.
615  7$aSuccessions (Matemātica)
615  7$aNombres, Teoria de.
615  7$aFuncions de variables complexes
615 14$aSequences, Series, Summability.
615 24$aFunctions of a Complex Variable.
615 24$aNumber Theory.
676   $a517.21
700   $aCandelpergher$b Bernard$4aut$4http://id.loc.gov/vocabulary/relators/aut$0739987
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9910257378903321
996   $aRamanujan summation of divergent series$91466442
997   $aUNINA