03340nam 22006015 450 99646654150331620200705131552.03-319-63630-810.1007/978-3-319-63630-6(CKB)4100000000587416(DE-He213)978-3-319-63630-6(MiAaPQ)EBC6299369(MiAaPQ)EBC5596509(Au-PeEL)EBL5596509(OCoLC)1004663268(PPN)204533260(EXLCZ)99410000000058741620170912d2017 u| 0engurnn|008mamaatxtrdacontentcrdamediacrrdacarrierRamanujan Summation of Divergent Series[electronic resource] /by Bernard Candelpergher1st ed. 2017.Cham :Springer International Publishing :Imprint: Springer,2017.1 online resource (XXIII, 195 p. 7 illus.) Lecture Notes in Mathematics,0075-8434 ;21853-319-63629-4 Introduction: 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.The 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.Lecture Notes in Mathematics,0075-8434 ;2185Sequences (Mathematics)Functions of complex variablesNumber theorySequences, Series, Summabilityhttps://scigraph.springernature.com/ontologies/product-market-codes/M1218XFunctions of a Complex Variablehttps://scigraph.springernature.com/ontologies/product-market-codes/M12074Number Theoryhttps://scigraph.springernature.com/ontologies/product-market-codes/M25001Sequences (Mathematics).Functions of complex variables.Number theory.Sequences, Series, Summability.Functions of a Complex Variable.Number Theory.517.21Candelpergher Bernardauthttp://id.loc.gov/vocabulary/relators/aut739987MiAaPQMiAaPQMiAaPQBOOK996466541503316Ramanujan summation of divergent series1466442UNISA02063nam 2200517I 450 991070660030332120171108081101.0(CKB)5470000002456439(OCoLC)1010746717(EXLCZ)99547000000245643920171108j200109 ua 0engurbn|||||||||txtrdacontentcrdamediacrrdacarrierTesting of densified liquid hydrogen stratification in a scale model propellant tank /John M. Jurns, Thomas M. Tomsik, William D. GreeneCleveland, Ohio :National Aeronautics and Space Administration, Glenn Research Center,September 2001.1 online resource (10 pages) illustrationsNASA/TM ;2001-209391"September 2001.""Prepared for the 1999 Cryogenic Engineering and International Cryogenic Materials Conference sponsored by the Advances in Cryogenic Engineering, Montreal, Quebec, Canada, July 12-16, 1999.""Performing organization: National Aeronautics and Space Administration, John H. Glenn Research Center at Lewis Field"--Report documentation page.Includes bibliographical references (page 10).Liquid hydrogennasatPropellant tanksnasatScale modelsnasatStratificationnasatCryogenic fluid storagenasatPerformance testsnasatLiquid hydrogen.Propellant tanks.Scale models.Stratification.Cryogenic fluid storage.Performance tests.Jurns John M.1408926Tomsik Thomas M.Greene William D.NASA Glenn Research Center,GPOGPOBOOK9910706600303321Testing of densified liquid hydrogen stratification in a scale model propellant tank3494096UNINA