Related papers: A product representation of pi

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.

We sometimes need to compute the most significant digits of the product of small integers with a multiplier requiring much storage: e.g., a large integer (e.g., $5^{100}$) or an irrational number ($\pi$). We only need to access the most…

In the present article a new method of deriving integral representations of combinations and partitions in terms of harmonic products has been established. This method may be relevant to statistical mechanics and to number theory.

The aim of this short paper is to give a practical introduction to functional interpretation of proofs for computer scientists interested in synthesis.

We describe the construction of the slice fibration of a given one.

These notes present an approach to obtaining the basic operations of addition and multiplication on the natural numbers in terms of elementary results about commutative monoids.

These are notes from a basic course in Several Complex Variables

This note presents an especially short and direct variant of Hermite's proof of the simple continued fraction expansion e = [2,1,2,1,1,4,1,1,6,...] and explains some of the motivation behind it.

This paper presents a new, significantly simpler proof of one of the main results of applied pi-calculus: the theorem that the concepts of observational and labeled equivalence of extended processes in applied pi-calculus coincide.

Two kinds of infinite product representations for Vign\'eras multiple gamma function are presented. As an application of these formulas, a multiplication formula for the function is derived.

We claim to resolve the P=?NP problem via a formal argument for P=NP.

Using a pointwise version of Fej\'{e}r's theorem about Fourier series, we obtain two formulae related to the series representations of positive integral powers of $\pi$. We also check the correctness of our formulae by the applications of…

In this note, we illustrate the computation of the approximation of the supply curves using a one-step basis. We derive the expression for the L2 approximation and propose a procedure for the selection of nodes of the approximation. We…

These are the notes from my courses on the arithmetic of quadratic forms.

It is shown that a piecewise linear function can be represented as a Max-Min polynomial of its linear components.

In this short note, we simply collect some known results about representing algebraic cycles by various kind of "nice" (e.g. smooth, local complete intersection, products of local complete intersection) algebraic cycles, up to rational…

A short proof of the linear nested Artin approximation property of the algebraic power series rings is given here.

The main purpose of this note is to pose a couple of problems which are easily formulated thought some seem to be not yet solved. These problems are of general interest for discrete mathematics including a new twig of a bough of theory of…

A short proof is given that the graphs with proper interval representations are the same as the graphs with unit interval representations.

In this note we observe that the notion of an induced representation has an analog for quasi-actions. We then use induced quasi-actions to refine some earlier rigidity results for product spaces.