Related papers: An Interesting Identity
I propose the index $h$, defined as the number of papers with citation number higher or equal to $h$, as a useful index to characterize the scientific output of a researcher.
The product sides of the Rogers--Ramanujan identities and alike often appear to be "transparently modular" (functions). The old work by Rogers (1894) and recent work by Rosengren make use (somewhat implicitly) of this fact for proving the…
We generalize aspects of Fourier Analysis from intervals on $\mathbb{R}$ to bounded and measurable subsets of $\mathbb{R}^n$. In doing so, we obtain a few interesting results. The first is a new proof of the famous Integral Cauchy-Schwarz…
A central problem in proof-theory is that of finding criteria for identity of proofs, that is, for when two distinct formal derivations can be taken as denoting the same logical argument. In the literature one finds criteria which are…
In this short note, we provide an elementary complex analytic method for converting known real integrals into numerous strange and interesting looking real integrals.
This paper describes a method to find a connection between combinatorial identities and hypergeometric series with a number of examples. Combinatorial identities can often be written as hypergeometric series with unit argument. In a number…
Source identities are fundamental identities between multivariable special functions. We give a geometric derivation of rational and trigonometric source identities. We also give a systematic derivation and extension of various determinant…
Motivated by the recent work of Chu [Electron. J. Combin. 17 (2010), #N24], we give simple proofs of Jensen's identity $$ \sum_{k=0}^{n}{x+kz\choose k}{y-kz\choose n-k} =\sum_{k=0}^{n}{x+y-k\choose n-k}z^k, $$ and Chu's and Mohanty-Handa's…
In this paper, we give an overview of the differential algebra approach to identifiability, and then note a very simple observation about input-output equivalence and identifiability, that describes the identifiability equivalence between…
This is a translation of Euler's 1773 "Variae observationes circa angulos in progressione geometrica progredientes", E561 in the Enestr{\"o}m index. I translated this paper as a result of my study of Euler's work on the infinite product…
The goal of this note is to construct, on many manifolds, non-trivial concordances from the identity to itself. This produces counterexamples to a recent conjecture by Botvinnik.
Identities of complex irreducible representations of finite groups can be explicitly constructed from character value sets. Among other things, these identities determine representations up to Gassmann equivalency. Some examples of…
Using a probabilistic approach, we derive some interesting combinatorial identities involving gamma and beta functions. These results generalize certain well-known combinatorial identities involving binomial coefficients and special…
Some finite series of harmonic numbers involving certain reciprocals are evaluated. Products of such reciprocals are expanded in a sum of the individual reciprocals, leading to a computer program. A list of examples is provided.
In this study, new master theorems and general formulas of integrals are presented and implemented to solve some complicated applications in different fields of science. The proposed theorems are considered to be generators of new problems,…
In 2015 Cristian-Silviu Radu designed an algorithm to detect identities of a class studied by Ramanujan and Kolberg. This class includes the famous identities by Ramanujan which provide a witness to the divisibility properties of $p(5n+4),$…
Fourier transformations of several functions of one and two variables are evaluated and then used to derive some integral and series identities. It is shown that certain double Mordell integrals can be reduced to a sum of products of…
We give an elementary probabilistic proof of a binomial identity. The proof is obtained by computing the probability of a certain event in two different ways, yielding two different expressions for the same quantity.
In this paper we give combinatorial proofs of some well known identities and obtain some generalizations. We give a visual proof of a result of Chapman and Costas-Santos regarding the determinant of sum of matrices. Also we find a new…
Stewart has presented a position-space derivation of the identity for the volume integral of a product of two vector fields noted by Gubarev, Stodolsky, and Zakharov, and applied the results to classical electromagnetic theory. I present a…