相关论文: On a problem of Bart Goddard
A systematic procedure for generating certain identities involving elementary symmetric functions is proposed. These identities, as particular cases, lead to new identities for binomial and q-binomial coefficients.
We solve two problems of analysis and special function theory recently posed by Furdui. The series in question are special cases in our solution.
Based on an interesting identity of Bat{\i}r we derive new identities for double sums involving famous number sequences. We also prove some double sum identities for binomial transform pairs.
Recently, Wang and Ma propose a conjecture associated with the possible generalization of Andrews-Warnaar identities. It is confirmed in this paper. As the applications of this conjecture, we prove that a family of series can be expressed…
We introduce the notion of irregular vertex (operator) algebras. The irregular versions of fundamental properties, such as Goddard uniqueness theorem, associativity and operator product expansions are formulated and proved. We also give…
Motivated by the substantial development of the special functions, we contribute to establish some rigorous results on the general series identities with bounded sequences and hypergeometric functions with different arguments, which are…
We give three elementary proofs of a nice equality of definite integrals, which arises from the theory of bivariate hypergeometric functions, and has connections with irrationality proofs in number theory. We furthermore provide a…
We give new generalizations of some q-series identities of Dilcher and Prodinger related to divisor functions. Some interesting special cases are also deduced, including an identity related to overpartitions studied by Corteel and Lovejoy.
In this paper we present a new identity and some of its variants which can be used for finding solutions while solving fractional infinite and finite series. We introduce another simple identity which is capable of generating solutions for…
Applying the theory of modular forms and Lambert series manipulations we establish an Eisenstein series identity. From this formula we confirm a Lambert series identity conjectured by Gosper. Another Lambert series identity of Gosper is…
Using basic hypergeometric functions and partial fraction decomposition we give a new kind of generalization of identities due to Uchimura, Dilcher, Van Hamme, Prodinger, and Chen-Fu related to divisor functions. An identity relating…
Using elementary means, we prove an identity giving the infinite product form of a sum of Lambert series originally stated by Venkatachaliengar, then rediscovered by Andrews, Lewis, and Liu. Then we derive two identities expressing certain…
In this series of seven papers, predominantly by means of elementary analysis, we establish a number of identities related to the Riemann zeta function. Whilst this paper is mainly expository, some of the formulae reported in it are…
Using elementary means, we prove several identities involving the M\"obius function, generalizing in the multidimensional case well-known formulas coming from convolution arguments.
We perform certain alternating binomial summations with parameters that occur in the analysis of algorithms. A combination of integral and special function and special number representations is used. The results are sufficiently general to…
In this paper, we consider the generating functions of the complete and elementary symmetric functions and provide a new generalization of these classical symmetric functions. Some classical relationships involving the complete and…
Based on a generalized Newton's identity, we construct a family of symmetric functions which deform the modular Hall-Littlewood functions. We also give a determinant formula for the Macdonald functions.
Our aim in this work is to give explicit formula of the linear processes solution of autoregressive time series AR(2) with hint of generating functions theory by using the Horadam numbers and polynomials.
We introduce a class of rational functions $A:\,\mathbb C\mathbb P^1\rightarrow \mathbb C\mathbb P^1$ which can be considered as a natural extension of the class of Latt\`es maps and establish basic properties of functions from this class.
In this series of seven papers, predominantly by means of elementary analysis, we establish a number of identities related to the Riemann zeta function. Whilst this paper is mainly expository, some of the formulae reported in it are…