Chan, Heng Huat; Wang, Liuquan Borweins’ cubic theta functions revisited. (English) Zbl 1501.33008 Ramanujan J. 57, No. 1, 55-70 (2022). MSC: 33E05 05A17 11E25 11F27 11P82 PDFBibTeX XMLCite \textit{H. H. Chan} and \textit{L. Wang}, Ramanujan J. 57, No. 1, 55--70 (2022; Zbl 1501.33008) Full Text: DOI
Chan, Heng Huat Theta functions, elliptic functions and \(\pi\). (English) Zbl 1458.11002 De Gruyter Graduate. Berlin: De Gruyter (ISBN 978-3-11-054071-0/pbk; 978-3-11-054191-5/ebook). xvi, 122 p. (2020). Reviewer: Franz Lemmermeyer (Jagstzell) MSC: 11-01 11F03 33D15 33E05 33C75 14H42 PDFBibTeX XMLCite \textit{H. H. Chan}, Theta functions, elliptic functions and \(\pi\). Berlin: De Gruyter (2020; Zbl 1458.11002) Full Text: DOI
Chan, Heng Huat Analogues of the Brent-Salamin algorithm for evaluating \(\pi\). (English) Zbl 1369.11108 Ramanujan J. 38, No. 1, 75-100 (2015). Reviewer: Ghaith A. Hiary (Columbus) MSC: 11Y60 33E05 11Y16 PDFBibTeX XMLCite \textit{H. H. Chan}, Ramanujan J. 38, No. 1, 75--100 (2015; Zbl 1369.11108) Full Text: DOI
Chan, Heng Huat; Chan, Song Heng; Liu, Zhi-Guo The Rogers-Ramanujan continued fraction and a new Eisenstein series identity. (English) Zbl 1170.33006 J. Number Theory 129, No. 7, 1786-1797 (2009). Reviewer: Mehdi Hassani (Zanjan) MSC: 11F03 11A55 11P84 33E05 11F11 11F20 11F27 PDFBibTeX XMLCite \textit{H. H. Chan} et al., J. Number Theory 129, No. 7, 1786--1797 (2009; Zbl 1170.33006) Full Text: DOI
Chan, Heng Huat; Cooper, Shaun Powers of theta functions. (English) Zbl 1231.11048 Pac. J. Math. 235, No. 1, 1-14 (2008). MSC: 11F11 05A19 11F20 11F27 33E05 PDFBibTeX XMLCite \textit{H. H. Chan} and \textit{S. Cooper}, Pac. J. Math. 235, No. 1, 1--14 (2008; Zbl 1231.11048) Full Text: DOI
Chan, Heng Huat; Cooper, Shaun Eisenstein series and theta functions to the septic base. (English) Zbl 1218.11043 J. Number Theory 128, No. 3, 680-699 (2008). MSC: 11F11 11F20 14K25 33E05 PDFBibTeX XMLCite \textit{H. H. Chan} and \textit{S. Cooper}, J. Number Theory 128, No. 3, 680--699 (2008; Zbl 1218.11043) Full Text: DOI
Baruah, N. D.; Berndt, B. C.; Chan, H. H. Ramanujan’s series for \(1/\pi\): a survey. (English) Zbl 1178.33003 Math. Stud. 2007, Spec. Centenary Vol., 1-24 (2007). MSC: 11Y60 11-02 33-02 33C20 33E05 11F27 PDFBibTeX XMLCite \textit{N. D. Baruah} et al., Math. Stud. 2007, 1--24 (2007; Zbl 1178.33003)
Chan, Heng Huat; Cooper, Shaun; Liaw, Wen-Chin The Rogers-Ramanujan continued fraction and a quintic iteration for \(1/\pi\). (English) Zbl 1141.11059 Proc. Am. Math. Soc. 135, No. 11, 3417-3424 (2007). Reviewer: Khodabakhsh Hessami Pilehrood (Shahrekord) MSC: 11Y60 11F20 11F27 11Y65 33E05 PDFBibTeX XMLCite \textit{H. H. Chan} et al., Proc. Am. Math. Soc. 135, No. 11, 3417--3424 (2007; Zbl 1141.11059) Full Text: DOI
Chan, Heng Huat; Cooper, Shaun; Toh, Pee Choon Ramanujan’s Eisenstein series and powers of Dedekind’s eta-function. (English) Zbl 1120.11021 J. Lond. Math. Soc., II. Ser. 75, No. 1, 225-242 (2007). Reviewer: Tom M. Apostol (Pasadena) MSC: 11F11 11F20 14K25 33D52 33E05 PDFBibTeX XMLCite \textit{H. H. Chan} et al., J. Lond. Math. Soc., II. Ser. 75, No. 1, 225--242 (2007; Zbl 1120.11021) Full Text: DOI
Chan, Heng Huat; Liu, Zhi-Guo Elliptic functions to the quintic base. (English) Zbl 1117.33012 Pac. J. Math. 226, No. 1, 53-64 (2006). Reviewer: Gabriele Nebe (Aachen) MSC: 33E05 11F11 11F27 PDFBibTeX XMLCite \textit{H. H. Chan} and \textit{Z.-G. Liu}, Pac. J. Math. 226, No. 1, 53--64 (2006; Zbl 1117.33012) Full Text: DOI
Chan, Heng Huat; Liu, Zhi-Guo; Ng, Say Tiong Circular summation of theta functions in Ramanujan’s lost notebook. (English) Zbl 1129.33006 J. Math. Anal. Appl. 316, No. 2, 628-641 (2006). Reviewer: Yilmaz Simsek (Antalya) MSC: 33D15 11F27 PDFBibTeX XMLCite \textit{H. H. Chan} et al., J. Math. Anal. Appl. 316, No. 2, 628--641 (2006; Zbl 1129.33006) Full Text: DOI
Chan, Heng Huat; Liu, Zhi-Guo; Ng, Say Tiong Elliptic functions and the quintuple, Hirschhorn and Winquist product identities. (English) Zbl 1081.33034 Int. J. Number Theory 1, No. 1, 33-43 (2005). Reviewer: Hari M. Srivastava (Victoria) MSC: 33E05 11B65 PDFBibTeX XMLCite \textit{H. H. Chan} et al., Int. J. Number Theory 1, No. 1, 33--43 (2005; Zbl 1081.33034) Full Text: DOI
Berndt, Bruce C.; Chan, Heng Huat; Zaharescu, Alexandru A quasi-theta product in Ramanujan’s lost notebook. (English) Zbl 1055.11015 Math. Proc. Camb. Philos. Soc. 135, No. 1, 11-18 (2003). Reviewer: Mark Sheingorn (New York) MSC: 11B65 33E05 33D15 33C75 11F30 PDFBibTeX XMLCite \textit{B. C. Berndt} et al., Math. Proc. Camb. Philos. Soc. 135, No. 1, 11--18 (2003; Zbl 1055.11015) Full Text: DOI
Chan, Heng Huat; Liu, Zhi-Guo Analogues of Jacobi’s inversion formula for the incomplete elliptic integral of the first kind. (English) Zbl 1018.33015 Adv. Math. 174, No. 1, 69-88 (2003). Reviewer: Shaun Cooper (Auckland) MSC: 33E05 33C60 33C05 PDFBibTeX XMLCite \textit{H. H. Chan} and \textit{Z.-G. Liu}, Adv. Math. 174, No. 1, 69--88 (2003; Zbl 1018.33015) Full Text: DOI
Chan, Heng Huat; Chua, Kok Seng; Solé, Patrick Quadratic iterations to \({\pi}\) associated with elliptic functions to the cubic and septic base. (English) Zbl 1021.11036 Trans. Am. Math. Soc. 355, No. 4, 1505-1520 (2003). Reviewer: R.Wegmann (Garching) MSC: 11Y60 33E05 33C05 11F03 PDFBibTeX XMLCite \textit{H. H. Chan} et al., Trans. Am. Math. Soc. 355, No. 4, 1505--1520 (2003; Zbl 1021.11036) Full Text: DOI
Chan, Heng Huat Ramanujan’s elliptic functions to alternative bases and approximations to \(\pi\). (English) Zbl 1140.11358 Bennett, M.A. (ed.) et al., Number theory for the millennium I. Proceedings of the millennial conference on number theory, Urbana-Champaign, IL, USA, May 21–26, 2000. Natick, MA: A K Peters (ISBN 1-56881-126-8/hbk). 197-213 (2002). Reviewer: Olaf Ninnemann (Berlin) MSC: 11Y60 11F27 33E05 PDFBibTeX XMLCite \textit{H. H. Chan}, in: Number theory for the millennium I. Proceedings of the millennial conference on number theory, Urbana-Champaign, IL, USA, May 21--26, 2000. Natick, MA: A K Peters. 197--213 (2002; Zbl 1140.11358)
Berndt, Bruce C.; Chan, Heng Huat; Kang, Soon-Yi; Zhang, Liang-Cheng A certain quotient of eta-functions found in Ramanujan’s lost notebook. (English) Zbl 1054.11022 Pac. J. Math. 202, No. 2, 267-304 (2002). MSC: 11F20 33E05 PDFBibTeX XMLCite \textit{B. C. Berndt} et al., Pac. J. Math. 202, No. 2, 267--304 (2002; Zbl 1054.11022) Full Text: DOI
Chan, Heng Huat; Liaw, Wen-Chin; Tan, Victor Ramanujan’s class invariant \(\lambda_ n\) and a new class of series for \(1/\pi\). (English) Zbl 1110.11300 J. Lond. Math. Soc., II. Ser. 64, No. 1, 93-106 (2001). Reviewer: Matti Vuorinen (Turku) MSC: 11F11 11F27 33E05 33C50 PDFBibTeX XMLCite \textit{H. H. Chan} et al., J. Lond. Math. Soc., II. Ser. 64, No. 1, 93--106 (2001; Zbl 1110.11300) Full Text: DOI
Berndt, Bruce C.; Chan, Heng Huat Eisenstein series and approximations to \(\pi\). (English) Zbl 0998.33003 Ill. J. Math. 45, No. 1, 75-90 (2001). Reviewer: Samuel James Patterson (Göttingen) MSC: 33C05 33E05 11F11 11R29 PDFBibTeX XMLCite \textit{B. C. Berndt} and \textit{H. H. Chan}, Ill. J. Math. 45, No. 1, 75--90 (2001; Zbl 0998.33003)
Berndt, Bruce C.; Chan, Heng Huat; Liaw, Wen-Chin On Ramanujan’s quartic theory of elliptic functions. (English) Zbl 1005.33009 J. Number Theory 88, No. 1, 129-156 (2001). Reviewer: Scott Ahlgren (Urbana) MSC: 33E05 11F27 11F20 PDFBibTeX XMLCite \textit{B. C. Berndt} et al., J. Number Theory 88, No. 1, 129--156 (2001; Zbl 1005.33009) Full Text: DOI
Berndt, Bruce C.; Chan, Heng Huat; Huang, Sen-Shan Incomplete elliptic integrals in Ramanujan’s lost notebook. (English) Zbl 0971.33012 Ismail, Mourad E. H. (ed.) et al., \(q\)-series from a contemporary perspective. AMS-IMS-SIAM joint summer research conference on \(q\)-series, combinatorics, and computer algebra, South Hadley, MA, USA, June 21-25, 1998. Providence, RI: American Mathematical Society. Contemp. Math. 254, 79-126 (2000). Reviewer: Shaun Cooper (Auckland) MSC: 33E05 11F27 11F03 05A19 PDFBibTeX XMLCite \textit{B. C. Berndt} et al., Contemp. Math. 254, 79--126 (2000; Zbl 0971.33012)
Chan, Heng Huat; Liaw, Wen-Chin Cubic modular equations and new Ramanujan-type series for \(1/\pi\). (English) Zbl 1125.11317 Pac. J. Math. 192, No. 2, 219-238 (2000). MSC: 11F11 11F27 33C50 33E05 11Y60 PDFBibTeX XMLCite \textit{H. H. Chan} and \textit{W.-C. Liaw}, Pac. J. Math. 192, No. 2, 219--238 (2000; Zbl 1125.11317) Full Text: DOI
Berndt, Bruce C.; Chan, Heng Huat Ramanujan and the modular \(j\)-invariant. (English) Zbl 0990.11022 Can. Math. Bull. 42, No. 4, 427-440 (1999). MSC: 11F03 33E05 33C05 11R20 11R29 PDFBibTeX XMLCite \textit{B. C. Berndt} and \textit{H. H. Chan}, Can. Math. Bull. 42, No. 4, 427--440 (1999; Zbl 0990.11022) Full Text: DOI
Berndt, Bruce C.; Chan, Heng Huat Notes on Ramanujan’s singular moduli. (English) Zbl 0936.33012 Gupta, Rajiv (ed.) et al., Number theory. Fifth conference of the Canadian Number Theory Association, Ottawa, Ontario, Canada, August 17-22, 1996. Providence, RI: American Mathematical Society. CRM Proc. Lect. Notes. 19, 7-16 (1999). Reviewer: Tom M.Apostol (Pasadena) MSC: 33E05 11F20 PDFBibTeX XMLCite \textit{B. C. Berndt} and \textit{H. H. Chan}, in: Number theory. Fifth conference of the Canadian Number Theory Association, Ottawa, Ontario, Canada, August 17--22, 1996. Providence, RI: American Mathematical Society. 7--16 (1999; Zbl 0936.33012)
Chan, Heng Huat; Ong, Yao Lin On Eisenstein series and \(\sum_{m,n=-\infty}^{\infty}q^{m^{2}+mn+2n^{2}}\). (English) Zbl 0922.11039 Proc. Am. Math. Soc. 127, No. 6, 1735-1744 (1999). Reviewer: Tom M. Apostol (Pasadena) MSC: 11F03 33E05 11Y60 PDFBibTeX XMLCite \textit{H. H. Chan} and \textit{Y. L. Ong}, Proc. Am. Math. Soc. 127, No. 6, 1735--1744 (1999; Zbl 0922.11039) Full Text: DOI
Chan, Heng Huat On Ramanujan’s cubic transformation formula for \(_2F_1(\frac 13;\frac 23;\text{\textbf{1}};z)\). (English) Zbl 0949.33002 Math. Proc. Camb. Philos. Soc. 124, No. 2, 193-204 (1998). Reviewer: Roland Girgensohn (Neuherberg) MSC: 33C05 11F11 33E05 PDFBibTeX XMLCite \textit{H. H. Chan}, Math. Proc. Camb. Philos. Soc. 124, No. 2, 193--204 (1998; Zbl 0949.33002) Full Text: DOI
Berndt, Bruce C.; Chan, Heng Huat; Zhang, Liang-Cheng Ramanujan’s singular moduli. (English) Zbl 0908.11024 Ramanujan J. 1, No. 1, 53-74 (1997). Reviewer: Tom M.Apostol (Pasadena) MSC: 11F20 33D10 33E05 PDFBibTeX XMLCite \textit{B. C. Berndt} et al., Ramanujan J. 1, No. 1, 53--74 (1997; Zbl 0908.11024) Full Text: DOI
Berndt, Bruce C.; Chan, Heng Huat; Zhang, Liang-Cheng Ramanujan’s remarkable product of theta-functions. (English) Zbl 0901.33007 Proc. Edinb. Math. Soc., II. Ser. 40, No. 3, 583-612 (1997). Reviewer: L.Lorentzen (Trondheim) MSC: 33D10 11F20 11F27 33E05 PDFBibTeX XMLCite \textit{B. C. Berndt} et al., Proc. Edinb. Math. Soc., II. Ser. 40, No. 3, 583--612 (1997; Zbl 0901.33007) Full Text: DOI
Berndt, Bruce C.; Chan, Heng Huat; Zhang, Liang-Cheng Ramanujan’s class invariants and cubic continued fraction. (English) Zbl 0843.11007 Acta Arith. 73, No. 1, 67-85 (1995). Reviewer: M.Sheingorn (New York) MSC: 11A55 33E05 11F03 PDFBibTeX XMLCite \textit{B. C. Berndt} et al., Acta Arith. 73, No. 1, 67--85 (1995; Zbl 0843.11007) Full Text: DOI EuDML