Related papers: Wallis's Formula and the Probability Integral

We show that Wahl's conjecture holds in all characteristics for a minuscule G/P.

The purpose of this short note is to present a simplified proof of Serre's modularity conjecture using the strong modularity lifting results currently available. This second version includes extra details on definitions and proofs than the…

We describe a statistical hypothesis test for the presence of a signal based on the likelihood ratio statistic. We derive the test for a case of interest and also show that for that case the test works very well, even far out in the tails…

In this article, we prove a weighted version of Saitoh's conjecture. As an application, we prove a weighted version of Saitoh's conjecture for higher derivatives.

(l) I have enough evidence to render the sentence S probable. (la) So, relative to what I know, it is rational of me to believe S. (2) Now that I have more evidence, S may no longer be probable. (2a) So now, relative to what I know, it is…

In this note, we find a new way to prove several properties of 2-alternating capacities.

We prove a recent conjecture by Ulas on reducible polynomial substitutions.

In this note we shall give a new proof to a quadrature formulae due to Newton.

The aim of this note is to show that Poincar\'e inequalities imply corresponding weighted versions in a quite general setting. Fractional Poincar\'e inequalities are considered, too. The proof is short and does not involve covering…

Recently, several researchers have claimed that conclusions obtained from a Bayes factor (or the posterior odds) may contradict those obtained from Bayesian posterior estimation. In this short paper, we wish to point out that no such…

Interpretation of the nonclassical total probability formula arising in some quantum experiments is provided based on stochastic models described by means of a sequence of random vectors changing in the measurement procedures.

In this note a general result is proved that can be used to evaluate exactly a class of highly oscillatory integrals.

I review the classical theory of likelihood based inference and consider how it is being extended and developed for use in complex models and sampling schemes.

We present a short, elementary proof not involving Fourier transforms of the theorem of Cram\'er and Wold that a Borel probability measure is determined by its values on half-spaces.

We present a probabilistic proof of Euler's pentagonal number theorem based on a shuffling model.

In this note we prove a weighted version of the Khintchine inequalities.

We present a slightly more general version of Boole's additive formula for factorials as a simple consequence of Lagrange's Interpolating Polynomial theorem.

This note is a somewhat-lighthearted comment on a recent paper by David Wallace, arXiv:0906.2718[quant-ph] entitled "A formal proof of the Born rule from decision-theoretic assumptions".

In this paper, we consider the poly-Bernoulli numbers and polynomials of the second kind and presents new and explicit formulae for calculating the poly-Bernoulli numbers of the second kind and the Stirling numbers of the second kind.

This paper proves a reciprocity formula for modular inverses for non-zero integers and demonstrates some applications of the reciprocity formula in calculating or verifying some modular inverses of specific forms, including the modular…