%0 Journal Article %T Quasi associated continued fractions and Hankel determinants of Dixon elliptic functions via Sumudu transform %A Kilicman, Adem %A Silambarasan, Rathinavel %A Altun, Omer %J Journal of Nonlinear Sciences and Applications %D 2017 %V 10 %N 7 %@ ISSN 2008-1901 %F Kilicman2017 %X In this work, Sumudu transform of Dixon elliptic functions for higher arbitrary powers \(sm^N(x, \alpha);N \geq 1, sm^N(x, \alpha)cm(x, \alpha); N \geq 0\) and \(sm^N(x, \alpha)cm^2(x, \alpha);N \geq 0\) by considering modulus \(\alpha \neq 0\) is obtained as three term recurrences and hence expanded as product of quasi associated continued fractions where the coefficients are functions of \(\alpha\). Secondly the coefficients of quasi associated continued fractions are used for Hankel determinants calculations by connecting the formal power series (Maclaurin series) and associated continued fractions. %9 journal article %R 10.22436/jnsa.010.07.49 %U http://dx.doi.org/10.22436/jnsa.010.07.49 %P 4000--4014 %0 Book %T Elliptic functions applied to conformal world maps %A O. S. Adams %D 1925 %I US Government Printing Office %C Washington %F Adams1925 %0 Journal Article %T Some determinants of Bernoulli %A W. A. Al-Salam %A L. Carlitz %J Euler and related numbers, Portugal. Math. %D 1959 %V 18 %F Al-Salam1959 %0 Journal Article %T Pseudo-factorials, elliptic functions, and continued fractions %A R. Bacher %A P. Flajolet %J Ramanujan J. %D 2009 %V 21 %F Bacher2009 %0 Journal Article %T Sumudu computation of the transient magnetic field in a lossy medium %A F. B. M. Belgacem %A E. H. Al-Shemas %A R. Silambarasan %J Appl. Math. Inf. Sci. %D 2017 %V 11 %F Belgacem2017 %0 Journal Article %T A distinctive Sumudu treatment of trigonometric functions %A F. B. M. Belgacem %A R. Silambarasan %J J. Comput. Appl. Math. %D 2017 %V 312 %F Belgacem2017 %0 Journal Article %T Further distinctive investigations of the Sumudu transform %A F. B. M. Belgacem %A R. Silambarasan %J AIP Conf. Proc. %D 2017 %V 1798 %F Belgacem2017 %0 Journal Article %T Sumudu transform of Dumont bimodular Jacobi elliptic functions for arbitrary powers %A F. B. M. Belgacem %A R. Silambarasan %J AIP Conf. Proc. %D 2017 %V 1798 %F Belgacem2017 %0 Journal Article %T Some orthogonal polynomials related to elliptic functions %A L. Carlitz %J Duke Math. J. %D 1960 %V 27 %F Carlitz1960 %0 Journal Article %T Some continued fraction expansions of Laplace transforms of elliptic functions %A E. V. F. Conrad %J Thesis (Ph.D.)–The Ohio State University, ProQuest LLC, Ann Arbor, MI %D 2002 %V %F Conrad2002 %0 Journal Article %T The Fermat cubic, elliptic functions, continued fractions, and a combinatorial excursion %A E. V. F. Conrad %A P. Flajolet %J Sém. Lothar. Combin. %D 2005/07 %V 54 %F Conrad2005/07 %0 Journal Article %T On the doubly periodic functions arising out of the curve \(x^3 + y^3 - 3\alpha xy = 1\) %A A. C. Dixon %J Quart. J. Pure Appl. Math. %D 1890 %V 24 %F Dixon1890 %0 Book %T The elementary properties of the elliptic functions, with examples %A A. C. Dixon %D 1894 %I Macmillan %C London and New York %F Dixon1894 %0 Book %T Le parametrage de la courbe d’equation \(x^3 + y^3 = 1\) %A D. Dumont %D 1988 %I Une introduction elementaire aux fonctions elliptiques %C preprint %F Dumont1988 %0 Journal Article %T On double sumudu transform and double Laplace transform %A H. Eltayeb %A A. Kılıçman %J Malays. J. Math. Sci. %D 2010 %V 4 %F Eltayeb2010 %0 Journal Article %T On integral transforms and matrix functions %A H. Eltayeb %A A. Kılıçman %A R. P. Agarwal %J Abstr. Appl. Anal. %D 2011 %V 2011 %F Eltayeb2011 %0 Journal Article %T Some continued fractions related to elliptic functions %A M. E. H. Ismail %A D. R. Masson %J Continued fractions: from analytic number theory to constructive approximation, Columbia, MO, (1998), Contemp. Math., Amer. Math. Soc., Providence, RI %D 1999 %V 236 %F Ismail1999 %0 Book %T Continued fractions %A W. B. Jones %A W. J. Thron %D 1980 %I Analytic theory and applications, With a foreword by Felix E. Browder, With an introduction by Peter Henrici, Encyclopedia of Mathematics and its Applications, Addison- Wesley Publishing Co. %C Reading, Mass. %F Jones1980 %0 Journal Article %T On a new integral transform and differential equations %A A. Kılıçman %A H. Eltayeb %J Math. Probl. Eng. %D 2010 %V 2010 %F Kılıçman2010 %0 Journal Article %T Some remarks on the Sumudu and Laplace transforms and applications to differential equations %A A. Kılıçman %A H. Eltayeb %J ISRN Appl. Math. %D 2012 %V 2012 %F Kılıçman2012 %0 Journal Article %T A note on the comparison between Laplace and Sumudu transforms %A A. Kılıçman %A H. Eltayeb %A K. A. M. Atan %J Bull. Iranian Math. Soc. %D 2011 %V 37 %F Kılıçman2011 %0 Journal Article %T On the solution of fractional Maxwell equations by Sumudu transform %A A. Kılıçman %A V. G. Gupta %A B. Shrama %J J. Math. Res. %D 2010 %V 2 %F Kılıçman2010 %0 Journal Article %T The trefoil %A J. C. Langer %A D. A. Singer %J Milan J. Math. %D 2014 %V 82 %F Langer2014 %0 Book %T Elliptic functions and applications %A D. F. Lawden %D 1989 %I Applied Mathematical Sciences, Springer-Verlag %C New York %F Lawden1989 %0 Book %T Continued fractions with applications %A L. Lorentzen %A H. Waadeland %D 1992 %I Studies in Computational Mathematics, North- Holland Publishing Co. %C Amsterdam %F Lorentzen1992 %0 Journal Article %T Implementation of the homotopy perturbation Sumudu transform method for solving Klein-Gordon equation %A A. M. Mahdy %A A. S. Mohamed %A A. A. Mtawa %J Appl. Math. %D 2015 %V 6 %F Mahdy2015 %0 Book %T Infinite families of exact sums of squares formulas, Jacobi elliptic functions, continued fractions, and Schur functions %A S. C. Milne %D 2002 %I Reprinted from Ramanujan J.,/ 6 (2002), 7–149 , With a preface by George E. Andrews, Developments in Mathematics, Kluwer Academic Publishers %C Boston, MA %F Milne 2002 %0 Book %T A treatise on the theory of determinants %A T. Muir %D 1960 %I Revised and enlarged by William H. Metzler, Dover Publications, Inc. %C New York %F Muir1960 %0 Journal Article %T Application of sumudu decomposition method for solving linear and nonlinear Klein- Gordon equations %A M. A. Ramadan %A M. S. Al-Luhaibi %J Int. J. Soft Comput. Eng. %D 2014 %V 3 %F Ramadan2014 %0 Journal Article %T Application of homotopy perturbation Sumudu transform method for solving heat and wave-like equations %A J. Singh %A D. Kumar %A A. Kilicman %J Malays. J. Math. Sci. %D 2013 %V 7 %F Singh2013 %0 Journal Article %T Note on the expansion of a power series into a continued fraction %A H. S. Wall %J Bull. Amer. Math. Soc. %D 1945 %V 51 %F Wall1945 %0 Book %T Analytic theory of continued fractions %A H. S. Wall %D 1948 %I D. Van Nostrand Company, Inc. %C New York, N. Y. %F Wall1948 %0 Journal Article %T A new integral transform with an application in heat-transfer problem %A X.-J. Yang %J Therm. Sci. %D 2016 %V 20 %F Yang2016 %0 Journal Article %T A new integral transform operator for solving the heat-diffusion problem %A X.-J. Yang %J Appl. Math. Lett. %D 2017 %V 64 %F Yang2017