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A continued fraction of order twelve

M. Mahadeva Naika, B. Dharmendra, K. Shivashankara (2008)

Open Mathematics

In this paper, we establish several explicit evaluations, reciprocity theorems and integral representations for a continued fraction of order twelve which are analogues to Rogers-Ramanujan’s continued fraction and Ramanujan’s cubic continued fraction.

A curious integral.

Masson, David R. (1996)

International Journal of Mathematics and Mathematical Sciences

A deformation of commutative polynomial algebras in even numbers of variables

Wenhua Zhao (2010)

Open Mathematics

We introduce and study a deformation of commutative polynomial algebras in even numbers of variables. We also discuss some connections and applications of this deformation to the generalized Laguerre orthogonal polynomials and the interchanges of right and left total symbols of differential operators of polynomial algebras. Furthermore, a more conceptual re-formulation for the image conjecture [18] is also given in terms of the deformed algebras. Consequently, the well-known Jacobian conjecture...

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