LEADER 04298nam 2200625 a 450 001 9910821090203321 005 20230802004439.0 010 $a1-280-37754-2 010 $a9786613555458 010 $a981-4366-46-3 035 $a(CKB)2550000000079949 035 $a(EBL)840716 035 $a(SSID)ssj0000598928 035 $a(PQKBManifestationID)12199193 035 $a(PQKBTitleCode)TC0000598928 035 $a(PQKBWorkID)10591601 035 $a(PQKB)11355927 035 $a(MiAaPQ)EBC840716 035 $a(WSP)00008252 035 $a(Au-PeEL)EBL840716 035 $a(CaPaEBR)ebr10524613 035 $a(CaONFJC)MIL355545 035 $a(OCoLC)877767895 035 $a(EXLCZ)992550000000079949 100 $a20120123d2012 uy 0 101 0 $aeng 135 $aurbn||||||||| 181 $ctxt 182 $cc 183 $acr 200 10$aDevelopment of elliptic functions according to Ramanujan /$foriginally by K. Venkatachaliengar ; edited and revised by Shaun Cooper 205 $a[Rev. ed.]. 210 $aSingapore ;$aHackensack, N.J. $cWorld Scientific$dc2012 215 $a1 online resource (185 p.) 225 1 $aMonographs in number theory,$x1793-8341 ;$vv. 6 300 $aOriginally published as a Technical Report 2 by Madurai Kamaraj University in February, 1988. 311 $a981-4366-45-5 320 $aIncludes bibliographical references and index. 327 $aPreface; Contents; 1. The Basic Identity; 1.1 Introduction; 1.2 The generalized Ramanujan identity; 1.3 The Weierstrass elliptic function; 1.4 Notes; 2. The Differential Equations of P, Q and R; 2.1 Ramanujan's differential equations; 2.2 Ramanujan's 1?1 summation formula; 2.3 Ramanujan's transcendentals U2n and V2n; 2.4 The imaginary transformation and Dedekind's eta-function; 2.5 Notes; 3. The Jordan-Kronecker Function; 3.1 The Jordan-Kronecker function; 3.2 The fundamental multiplicative identity; 3.3 Partitions; 3.4 The hypergeometric function 2F1(1/2, 1/2; 1; x): first method 327 $a3.5 Notes 4. The Weierstrassian Invariants; 4.1 Halphen's differential equations; 4.2 Jacobi's identities and sums of two and four squares; 4.3 Quadratic transformations; 4.4 The hypergeometric function 2F1(1/2, 1/2; 1; x): second method; 4.5 Notes; 5. The Weierstrassian Invariants, II; 5.1 Parameterizations of Eisenstein series; 5.2 Sums of eight squares and sums of eight triangular numbers; 5.3 Quadratic transformations; 5.4 The hypergeometric function 2F1(1/4, 3/4; 1; x); 5.5 The hypergeometric function 2F1(1/6, 5/6; 1; x); 5.6 The hypergeometric function 2F1(1/3, 2/3; 1; x) 327 $a5.7 Notes 6. Development of Elliptic Functions; 6.1 Introduction; 6.2 Jacobian elliptic functions; 6.3 Reciprocals and quotients; 6.4 Derivatives; 6.5 Addition formulas; 6.6 Notes; 7. The Modular Function ?; 7.1 Introduction; 7.2 Modular equations; 7.3 Modular equation of degree 3; 7.4 Modular equation of degree 5; 7.5 Modular equation of degree 7; 7.6 Modular equation of degree 11; 7.7 Modular equation of degree 23; 7.8 Notes; Appendix A Singular Moduli; A.1 Notes; Appendix B The Quintuple Product Identity; B.1 Notes; Appendix C Addition Theorem of Elliptic Integrals; Bibliography; Index 330 $aThis unique book provides an innovative and efficient approach to elliptic functions, based on the ideas of the great Indian mathematician Srinivasa Ramanujan. The original 1988 monograph of K Venkatachaliengar has been completely revised. Many details, omitted from the original version, have been included, and the book has been made comprehensive by notes at the end of each chapter. The book is for graduate students and researchers in Number Theory and Classical Analysis, as well for scholars and aficionados of Ramanujan's work. It can be read by anyone with some undergraduate knowledge of 410 0$aMonographs in number theory ;$vv. 6. 606 $aElliptic functions 615 0$aElliptic functions. 676 $a515.983 700 $aVenkatachaliengar$b K$01687401 701 $aCooper$b Shaun$0767406 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910821090203321 996 $aDevelopment of elliptic functions according to Ramanujan$94060821 997 $aUNINA