LEADER 09394cam 2200853 a 4500001 ocm60320109 003 OCoLC 005 20181106141622.8 008 050405m20052018nyuc b 001 0 eng 010 2005923547 040 UKM |beng |cUKM |dOHX |dBAKER |dDLC |dIXA |dMBB |dYDXCP |dBTCTA |dOCLCG |dMUQ |dBDX |dUKMGB |dNHM |dOCLCO |dMUU |dGEBAY |dXFF |dOCLCF |dOCLCO |dOCLCQ |dOCLCO |dOCLCQ |dNJR |dDHA |dOCLCQ |dIPL |dCLS |dOCLCA |dINU 019 312483730 020 9780387255293 |q(pt. 1 ; |qhardcover) 020 038725529X |q(pt. 1 ; |qhardcover) 020 9780387777658 |q(pt. 2 ; |qhardcover) 020 0387777652 |q(pt. 2 ; |qhardcover) 020 9781461438090 |q(pt. 3 ; |qhardcover) 020 1461438098 |q(pt. 3 ; |qhardcover) 020 9781461440802 |q(pt. 4 ; |qhardcover) 020 1461440807 |q(pt. 4 ; |qhardcover) 020 9783319778327 |q(pt. 5 ; |qhardcover) 020 3319778323 |q(pt. 5 ; |qhardcover) 020 |z9780387281247 |q(pt. 1 ; |qebook) 020 |z038728124X |q(pt. 1 ; |qebook) 020 |z9780387777665 |q(pt. 2 ; |qebook) 020 |z0387777660 |q(pt. 2 ; |qebook) 020 |z9781461438106 |q(pt. 3 ; |qebook) 020 |z1461438101 |q(pt. 3 ; |qebook) 020 |z9781461440819 |q(pt. 4 ; |qebook) 020 |z1461440815 |q(pt. 4 ; |qebook) 020 |z9783319778341 |q(pt. 5 ; |qebook) 020 |z331977834X |q(pt. 5 ; |qebook) 024 3 9780387255293 035 40028835326 035 (OCoLC)60320109 |z(OCoLC)312483730 042 ukblsr 043 a-ii--- 050 00 QA29.R3 |bA73 2005 072 7 QA |2lcco 082 04 510 |222 100 1 Andrews, George E., |d1938- |=^A27682 245 10 Ramanujan's lost notebook / |cGeorge E. Andrews, Bruce C. Berndt. 260 New York ;London : |bSpringer, |c2005-2018. 300 5 volumes : |bportraits ; |c25 cm 336 text |btxt |2rdacontent 337 unmediated |bn |2rdamedia 338 volume |bnc |2rdacarrier 504 Includes bibliographical references and indexes. 505 00 |tThe Rogers-Ramanujan Continued Fraction and Its Modular Properties -- |tTwo-Variable Generalizations of (1.1.10) and (1.1.11) -- |tHybrids of (1.1.10) and (1.1.11) -- |tFactorizations of (1.1.10) and (1.1.11) -- |tModular Equations -- |tTheta-Function Identities of Degree 5 -- |tRefinements of the Previous Identities -- |tIdentities Involving the Parameter k = R(q)R[superscript 2](q[superscript 2]) -- |tOther Representations of Theta Functions Involving R(q) -- |tExplicit Formulas Arising from (1.1.11) -- |tExplicit Evaluations of the Rogers-Ramanujan Continued Fraction -- |tExplicit Evaluations Using Eta-Function Identities -- |tGeneral Formulas for Evaluating R [characters not reproducible] and S [characters not reproducible] -- |tPage 210 of Ramanujan's Lost Notebook -- |tSome Theta-Function Identities -- |tRamanujan's General Explicit Formulas for the Rogers-Ramanujan Continued Fraction -- |tA Fragment on the Rogers-Ramanujan and Cubic Continued Fractions -- |tThe Rogers-Ramanujan Continued Fraction -- |tThe Theory of Ramanujan's Cubic Continued Fraction -- |tExplicit Evaluations of G(q) -- |tThe Rogers-Ramanujan Continued Fraction and Its Partitions and Lambert Series -- |tConnections with Partitions -- |tFurther Identities Involving the Power Series Coefficients of C(q) and 1/C(q) -- |tGeneralized Lambert Series -- |tFurther q-Series Representations for C(q) -- |tFinite Rogers-Ramanujan Continued Fractions -- |tFinite Rogers-Ramanujan Continued Fractions -- |tA generalization of Entry 5.2.1 -- |tClass Invariants -- |tA Finite Generalized Rogers-Ramanujan Continued Fraction. 505 80 |tOther q-continued Fractions -- |tThe Main Theorem -- |tA Second General Continued Fraction -- |tA Third General Continued Fraction -- |tA Transformation Formula -- |tZeros -- |tTwo Entries on Page 200 of Ramanujan's Lost Notebook -- |tAn Elementary Continued Fraction -- |tAsymptotic Formulas for Continued Fractions -- |tThe Main Theorem -- |tTwo Asymptotic Formulas Found on Page 45 of Ramanujan's Lost Notebook -- |tAn Asymptotic Formula for R(a,q) -- |tRamanujan's Continued Fraction for (q[superscript 2];q[superscript 3])[infinity]/(q;q[superscript 3])[infinity] -- |tA Proof of Ramanujan's Formula (8.1.2) -- |tThe Special Case a = w of (8.1.2) -- |tTwo Continued Fractions Related to (q[superscript 2];q[superscript 3])[infinity]/(q;q[superscript 3])[infinity] -- |tAn Asymptotic Expansion -- |tThe Rogers-Fine Identity -- |tSeries Transformations -- |tThe Series [characters not reproducible] -- |tThe Series [characters not reproducible] -- |tThe Series [characters not reproducible] -- |tAn Empirical Study of the Rogers-Ramanujan Identities -- |tThe First Argument -- |tThe Second Argument -- |tThe Third Argument -- |tThe Fourth Argument -- |tRogers-Ramanujan-Slater-Type Identities -- |tIdentities Associated with Modulus 5 -- |tIdentities Associated with the Moduli 3, 6, and 12 -- |tIdentities Associated with the Modulus 7 -- |tFalse Theta Functions -- |tPartial Fractions -- |tThe Basic Partial Fractions -- |tApplications of the Partial Fraction Decompositions -- |tPartial Fractions Plus -- |tRelated Identities -- |tRemarks on the Partial Fraction Method -- |tHadamard Products for Two q-Series. 505 80 |tStieltjes-Wigert Polynomials -- |tThe Hadamard Factorization -- |tSome Theta Series -- |tA Formal Power Series -- |tThe Zeros of K[subscript infinity](zx) -- |tSmall Zeros of K[subscript infinity](z) -- |tA New Polynomial Sequence -- |tThe Zeros of p[subscript n](a) -- |tA Theta Function Expansion -- |tRamanujan's Product for p[subscript infinity](a) -- |tIntegrals of Theta Functions -- |tPreliminary Results -- |tThe Identities on Page 207 -- |tIntegral Representations of the Rogers-Ramanujan Continued Fraction -- |tIncomplete Elliptic Integrals -- |tPreliminary Results -- |tTwo Simpler Integrals -- |tElliptic Integrals of Order 5 (I) -- |tElliptic Integrals of Order 5 (II) -- |tElliptic Integrals of Order 5 (III) -- |tElliptic Integrals of Order 15 -- |tElliptic Integrals of Order 14 -- |tAn Elliptic Integral of Order 35 -- |tConstructions of New Incomplete Elliptic Integral Identities -- |tInfinite Integrals of q-Products -- |tProofs -- |tModular Equations in Ramanujan's Lost Notebook -- |tEta-Function Identities -- |tSummary of Modular Equations of Six Kinds -- |tA Fragment on Page 349 -- |tFragments on Lambert Series -- |tEntries from the Two Fragments -- |tLocation Guide -- |tProvenance. 520 This 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. 600 10 Ramanujan Aiyangar, Srinivasa, |d1887-1920. |=^A68821 600 17 Ramanujan Aiyangar, Srinivasa, |d1887-1920 |2fast |0(OCoLC)fst00018044 |?UNAUTHORIZED 600 17 Ramanujan Aiyangar, Srinivasa. |2swd |?UNAUTHORIZED 650 0 Mathematics. |=^A2085 650 0 Mathematical analysis. |=^A18530 650 0 Number theory. |=^A22877 650 0 Mathematicians |zIndia |vBiography. |=^A1181339 650 7 Mathematical analysis. |2fast |0(OCoLC)fst01012068 650 7 Mathematicians. |2fast |0(OCoLC)fst01012154 650 7 Mathematics. |2fast |0(OCoLC)fst01012163 650 7 Number theory. |2fast |0(OCoLC)fst01041214 651 7 India. |2fast |0(OCoLC)fst01210276 |?UNAUTHORIZED 650 07 Q.-Serie. |2swd 648 7 Geschichte 1900-1920 |2swd 655 7 Biography. |2fast |0(OCoLC)fst01423686 700 1 Berndt, Bruce C., |d1939- |=^A244057 949 |i30372016668912 |ojjlm 960 |o1 |s109.00 |tJoyner48 |uJAPP |zUSD 993 pt. 5 596 1 998 5046187