Related papers: A simple proof of Tong's theorem

Following suggestions of T. H. Koornwinder, we give a new proof of Kummer's theorem involving Zeilberger's algorithm, the WZ method and asymptotic estimates. In the first section, we recall a classical proof given by L. J. Slater. The…

We provide a simple proof of Kamp's theorem.

We give a new simpler proof of a theorem of Jayne and Rogers.

In this expository article we provide an elegant proof of the one-sided Ingham-Karamata Tauberian theorem. As an application, we present a short deduction of the prime number theorem.

We present an elementary proof of the fundamental theorem of algebra, following Cauchy's version but avoiding his use of circular functions. It is written in the same spirit as Littlewood's proof of 1941, but reduces it to more elementary…

We give a simple proof of Kolmogorov's theorem on the persistence of a quasiperiodic invariant torus in Hamiltonian systems. The theorem is first reduced to a well-posed inversion problem (Herman's normal form) by switching the frequency…

We give a pen and paper and (comparatively) much simpler proof to verify of the Four Colour Theorem.

I present a simple, elementary proof of Morley's theorem, highlighting the naturalness of this theorem.

In this short note, we give a simple proof of a Lee-Yang type theorem which appeared in "Lee-Yang theorems and the complexity of computing averages" by Alistair Sinclair and Piyush Srivastava.

We present a proof of the Sturm-Hurwitz theorem, using basic calculus.

We give a remarkably elementary proof of the Brouwer fixed point theorem. The proof is verifiable for most of the mathematicians.

Myriad articles are devoted to Mertens's theorem. In yet another, we merely wish to draw attention to a proof by Hardy, which uses a Tauberian theorem of Landau that "leads to the conclusion in a direct and elegant manner". Hardy's proof is…

In this paper, we give a new and short proof of a Theorem on k-hypertournament losing scores due to Zhou et al.[7].

This expository note presents a constructive proof of Wigner's theorem using only a few basic facts about Hilbert spaces, such as the existence of orthonormal bases and the Fourier decomposition of a vector. Our proof is based on a proof by…

We provide a simple and short proof of the Karush-Kuhn-Tucker theorem with finite number of equality and inequality constraints. The proof relies on an elementary linear algebra lemma and the local inverse theorem.

We give a short proof of a theorem of J.-E. Pin (theorem 1.1 below), which can be found in his thesis. The part of the proof which is my own (not Pin's) is a complete replacement of the same part in an earlier version of this paper.

We give a new proof of the theorem of Kronecker-Weber based on Kummer theory and Stickelberger's theorem.

In the current note, we present a new, short proof of the famous AM-GM-HM inequality using only induction and basic calculus.

We give here a new proof of a Tauberian Theorem of complex Laplace transform using the Theory of measure and theory of function with bounded variations. However we deduce the simple proof of Prime Number Theorem.

A new simple proof of Stirling's formula via the partial fraction expansion for the tangent function is presented.