An analytic proof of the Borwein Conjecture

We provide a proof of the Borwein Conjecture using analytic methods.

[1]  George E. Andrews,et al.  On a Conjecture of Peter Borwein , 1995, J. Symb. Comput..

[2]  George E. Andrews,et al.  Partitions with Prescribed Hook Differences , 1987, Eur. J. Comb..

[3]  Roderick Wong,et al.  Asymptotic approximations of integrals , 1989, Classics in applied mathematics.

[4]  Alexander Berkovich,et al.  Positivity preserving transformations for $q$-binomial coefficients , 2003 .

[5]  Alexander Berkovich,et al.  Dissecting the Stanley partition function , 2005, J. Comb. Theory, Ser. A.

[6]  Christian Stump.  q,t-Fuß–Catalan numbers for finite reflection groups , 2009, 0901.1574.

[7]  The generalized Borwein conjecture. I. The Burge transform , 2000, math/0011220.

[8]  David M. Bressoud,et al.  Some identities for terminating q-series , 1981, Mathematical Proceedings of the Cambridge Philosophical Society.

[9]  David M. Bressoud.  The Borwein conjecture and partitions with prescribed hook differences , 1996, Electron. J. Comb..

[10]  S. Ole Warnaar.  The generalized Borwein conjecture. II. Refined q-trinomial coefficients , 2003, Discret. Math..

[11]  Philippe Flajolet,et al.  Analytic Combinatorics , 2009 .

[12]  W. N. Bailey.  Some Identities in Combinatory Analysis , 1946 .

[13]  Jiyou Li.  A note on the Borwein conjecture , 2015 .

[14]  Dennis Stanton,et al.  Lattice Paths and Positive Trigonometric Sums , 1999 .

[15]  .. I. T. B. Transform.  THE GENERALIZED BORWEIN CONJECTURE , 2011 .

[16]  이현주.  Q. , 2005 .

[17]  Basil Gordon,et al.  A COMBINATORIAL GENERALIZATION OF THE ROGERS-RAMANUJAN IDENTITIES.* , 1961 .

[18]  THE LIMITING DISTRIBUTION OF THE COEFFICIENTS OF THE q-CATALAN NUMBERS , 2007, 0708.2574.

[19]  G. Bhatnagar,et al.  A Partial Theta Function Borwein Conjecture , 2019, Trends in Mathematics.