Related papers: Variations on Ramanujan's nested radicals

The Ramanujan Machine project predicts new continued fraction representations of numbers expressed by important mathematical constants. Generally, the value of a continued fraction is found by reducing it to a second order linear difference…

We study a number of possible extensions of the Ramanujan master theorem, which is formulated here by using methods of Umbral nature. We discuss the implications of the procedure for the theory of special functions, like the derivation of…

We give a generalization of a Ramanujan's exercise for high school students. Our results can be regarded as a variation of the factorization formula of $x^{n} - 1$.

Ramanujan Master Theorem is a technique developed by the indian mathematician S. Ramanujan to evaluate a class of definite integrals. This technique is used here to calculate the values of integrals associated with specific Feynman…

A number theoretical model of $1/f$ noise found in phase locked loops is developed. The dynamics of phases and frequencies involved in the nonlinear mixing of oscillators and the low-pass filtering is formulated thanks to the rules of the…

In this article with the help of the inverse function of the singular moduli we evaluate the Rogers Ranmanujan continued fraction and his first derivative.

The classical quadratic formula and some of its lesser known variants for solving the quadratic equation are reviewed. Then, a new formula for the roots of a quadratic polynomial is presented.

This paper introduces a Ramanujan inner product and its corresponding norm, establishing a novel framework for the stability analysis of hybrid and discrete-time systems as an alternative to traditional Euclidean metrics. We establish new…

In the present paper, we introduce a multiple Ramanujan sum for arithmetic functions, which gives a multivariable extension of the generalized Ramanujan sum studied by D. R. Anderson and T. M. Apostol. We then find fundamental arithmetic…

Recently, a construction of minimal codes arising from a family of almost Ramanujan graphs was shown. Ramanujan graphs are examples of expander graphs that minimize the second-largest eigenvalue of their adjacency matrix. We call such…

The overlap of Srinivasa Ramanujan's work with quantum field theory is discussed. A mathematically natural axiom for euclidean quantum field theories is proposed.

In Ramanujan's Lost Notebook there is an amazing identity that furnishes infinitely many "almost counterexamples" to the cubic Fermat's Last Theorem, with no indication whatsoever how he discovered it. In 1995, Michael Hirschhorn explained,…

We prove that there exist bipartite, biregular Ramanujan graphs of every degree and every number of vertices provided that the cardinalities of the two sets of the bipartition divide each other. This generalizes a result of Marcus,…

We prove some results on the distance between two perfect numbers using Ramanujan-Nagell type equations.

In this paper, we combined two types of partitions and introduced 2-colored Rogers-Ramanujan partitions. By finding some functional equations and using a constructive method, some identities have been found. Some Overpartition identities…

The status of our understanding of relativistic sum rules is reviewed. The recent development of new theoretical methods for the evaluation of these sum rules offers hope for further advances in this challenging field. These new techniques…

We develop the theory of copartitions, which are a generalization of partitions with connections to many classical topics in partition theory, including Rogers-Ramanujan partitions, theta functions, mock theta functions, partitions with…

We suggest a continued fraction origin to Ramanujan's approximation to {(a-b)/(a+b)}^2 in terms of the arc length of an ellipse with semiaxes a and b. Moreover, we discuss the asymptotic accuracy of the approximation.

We prove a number of new Rogers-Ramanujan type identities involving double, triple and quadruple sums. They were discovered after an extensive search using Maple. The main idea of proofs is to reduce them to some known identities in the…

We use a q-series identity by Ramanujan to give a combinatorial interpretation of Ramanujan's tau function which involves t-cores and a new class of partitions which we call (m,k)-capsids. The same method can be applied in conjunction with…