相关论文: Applications of Wallis Theorem

In this paper the double-sided Talor's approximations are used to obtain generalisations and improvements of some trigonometric inequalities.

In this note we show that any proof of Wallis's formula or of the probability integral formula proves both assertions.

The goal of this Section is to formulate some of the basic results on the theory of integral equations and mention some of its applications. The literature of this subject is very large. Proofs are not given due to the space restriction.…

In this paper, we present new applications of our general minimax theorems. In particular, one of them concerns the multiplicity of global minima for the integral functional of the Calculus of Variations.

In this work we state a Theorem on number theory and apply it to solve some ordinary and partial differential equations.

In the present paper we introduce old and new results related to St\"ormer theorem about Pell equations. Moreover we give four types of applications of these results.

In this article we present a generalization of a Leibniz's geometrical theorem and an application of it.

In this article we use the Desargues' theorem and its reciprocal to solve two problems.

We extend the equivalence of the Salem type for the Riemann hypothesis by application of Titchmarsh's theorem. Other equivalences to the Riemann hypothesis and notes on related Fourier integrals are provided.

We extend the authors' previous work on Wiener-Wintner double recurrence theorem to the case of polynomials.

We present generalisations of Wilson's theorem for double factorials, hyperfactorials, subfactorials and superfactorials.

This paper deals with the evaluation of some definite Euler-type integrals in terms of the Wright hypergeometric function. We obtain a theorem on the Wright hypergeometric function and then use this theorem to evaluate some definite…

A description of solutions of some integral equations has been obtained. A two-radii theorem is obtained as well.

In this lecture notes we try to familiarize the audience with the theory of Bernoulli polynomials; we study their properties, and we give, with proofs and references, some of the most relevant results related to them. Several applications…

In this paper we prove the WALA conjecture.

We give an elementary proof of Kelley's theorem based on a minimax argument. Some applications to related problems are also developed.

We discuss a version of the fundamental theorem of calculus in several variables and some applications, of potential interest as a teaching material in undergraduate courses.

The survey presents the well-known Warshall's algorithm, a generalization and some interesting applications of this.

We give exposition of a Liouville theorem established in \cite{Li3} which is a novel extension of the classical Liouville theorem for harmonic functions. To illustrate some ideas of the proof of the Liouville theorem, we present a new proof…

In this note, we consider applications of Ratner's theorem to constructions of families of polynomials with dense values on the set of primitive integer points from the viewpoint of invariant theory.