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020 _a9780387281247
_9978-0-387-28124-7
024 7 _a10.1007/038728124-X
_2doi
035 _avtls000330497
039 9 _a201509030722
_bVLOAD
_c201404120453
_dVLOAD
_c201404090235
_dVLOAD
_c201401311343
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_zstaff
_wmsplit0.mrc
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050 4 _aQA564-609
100 1 _aAndrews, George E.
_eautor
_9302553
245 1 0 _aRamanujan’s Lost Notebook :
_bPart I /
_cby George E. Andrews, Bruce Berndt.
264 1 _aNew York, NY :
_bSpringer New York,
_c2005.
300 _aXIV, 437 páginas,
_brecurso en línea.
336 _atexto
_btxt
_2rdacontent
337 _acomputadora
_bc
_2rdamedia
338 _arecurso en línea
_bcr
_2rdacarrier
347 _aarchivo de texto
_bPDF
_2rda
500 _aSpringer eBooks
505 0 _aInroduction -- Rogers-Ramanujan Continued Fraction and Its Modular Properties -- Explicit Evaluations of the Rogers-Ramanujan Continued Fraction -- A Fragment on the Rogers-Ramanujan and Cubic Continued Fractions -- The Rogers-Ramanujan Continued Fraction and Its Connections with Partitions and Lambert Series -- Finite Rogers-Ramanujan Continued Fractions -- Other q-continued Fractions -- Asymptotic Formulas for Continued Fractions -- Ramanujan’s Continued Fraction for (q2;q3)?/(q;q3)? -- The Rogers-Fine Identity -- An Empirical Study of the Rogers-Ramanujan Identities -- Rogers-Ramanujan-Slater Type Identities -- Partial Fractions -- Hadamard Products for Two q-Series -- Integrals of Theta Functions -- Incomplete Elliptic Integrals -- Infinite Integrals of q-Products -- Modular Equations in Ramanujan’s Lost Notebook -- Fragments on Lambert Series.
520 _aThis volume is the first of approximately four volumes devoted to providing statements, proofs, and discussions of all the claims made by Srinivasa Ramanujan in his lost notebook and all his other manuscripts and letters published with the lost notebook. In addition to the lost notebook, this publication contains copies of unpublished manuscripts in the Oxford library, in particular, his famous unpublished manuscript on the partition and tau-functions; fragments of both published and unpublished papers; miscellaneous sheets; and Ramanujan's letters to G. H. Hardy, written from nursing homes during Ramanujan's final two years in England. This volume contains accounts of 442 entries (counting multiplicities) made by Ramanujan in the aforementioned publication. The present authors have organized these claims into eighteen chapters, containing anywhere from two entries in Chapter 13 to sixty-one entries in Chapter 17. Most of the results contained in Ramanujan's Lost Notebook fall under the purview of q-series. These include mock theta functions, theta functions, partial theta function expansions, false theta functions, identities connected with the Rogers-Fine identity, several results in the theory of partitions, Eisenstein series, modular equations, the Rogers-Ramanujan continued fraction, other q-continued fractions, asymptotic expansions of q-series and q-continued fractions, integrals of theta functions, integrals of q-products, and incomplete elliptic integrals. Other continued fractions, other integrals, infinite series identities, Dirichlet series, approximations, arithmetic functions, numerical calculations, diophantine equations, and elementary mathematics are some of the further topics examined by Ramanujan in his lost notebook.
590 _aPara consulta fuera de la UANL se requiere clave de acceso remoto.
700 1 _aBerndt, Bruce.
_eautor
_9302554
710 2 _aSpringerLink (Servicio en línea)
_9299170
776 0 8 _iEdición impresa:
_z9780387255293
856 4 0 _uhttp://remoto.dgb.uanl.mx/login?url=http://dx.doi.org/10.1007/0-387-28124-X
_zConectar a Springer E-Books (Para consulta externa se requiere previa autentificación en Biblioteca Digital UANL)
942 _c14
999 _c278735
_d278735