Related papers: Another proof of Bailey's 6-psi-6 summation
We give an alternate proof of three versions of the theorem on extrapolation of Carleson measures.
For Fatou's interpolation theorem of 1906 we suggest a new elementary proof.
Euler--Maclaurin and Poisson analogues of the summations $\sum_{a < n \leq b} \chi(n) f(n)$, $\sum_{a < n \leq b} d(n) f(n)$, $\sum_{a < n \leq b} d(n) \chi (n) f(n)$ have been obtained in a unified manner, where $(\chi (n))$ is a periodic…
A simple proof of Euler's formula which states that the sum of the reciprocals of all natural numbers squared equals $\pi^2/6$ is presented based on the distribution theory introduced by Laurent Schwartz. Additional identities are obtained…
An expansion formula of a new type with the rest term of Cauchy type is derived in the operator formulation of generalized umbral calculus
We give an elementary, self-contained and quick proof of Belyi's theorem. As a by-product of our proof we obtain an explicit bound for the degree of the defining number field of a Belyi surface.
We present some congruences modulo $p^{6-d}$ for sums of the type $\sum_{k=0}^{(p-3)/2}x^k{2k\choose k}/(2k+1)^d$, for $d=1,2,3$ where $p>5$ is a prime.
A generalization of the q-(Pfaff)-Saalschutz summation formula is proved. This implies a generalization of the Burge transform, resulting in an additional dimension of the ``Burge tree''. Limiting cases of our summation formula imply the…
Extends previous work on a quintic-solving algorithm to equations of the eighth-degree.
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…
We introduce the notions of generalized and weighted generalized $\psi$-estimators as unique points of sign change of some appropriate functions, and we give necessary as well as sufficient conditions for their existence. We also derive a…
Rejoinder of "On the Birnbaum Argument for the Strong Likelihood Principle" by Deborah G. Mayo [arXiv:1302.7021].
In this paper, we present the character analogue of the Boole summation formula. Using this formula, an integral representation is derived for the alternating Dirichlet $L-$function and its derivative is evaluated at $s=0$. Some…
We give a new proof of a lemma by L. Shepp, that was used in connection to random coverings of a circle.
In this article we survey some recent extensions and generalisations of the celebrated Mass Transference Principle (Beresnevich and Velani, Annals of Mathematics, 2006).
A great number of articles widen a known scientific result $P(a)$ (such as: a theorem, an inequality, or a math/physics/chemical etc. proposition or formula) by a simple recurrence procedure and using, in the proof, the proposition $P(a)$…
We give an extension of Sister Celine's method of proving hypergeometric sum identities that allows it to handle a larger variety of input summands. We then apply this to several problems. Some give new results, and some reprove already…
This memoir is a survey of theorems and inequalities which have grown out of, and extended, the seminal estimate of Montgomery \cite{HM70} \begin{multline*} V(x,Q)=\sum_{q\le Q}\sum_{\substack{a=1\\ (a,q)=1}}^q \left| \psi(x;q,a) -…
This paper suggests a new interpretation of the Dempster-Shafer theory in terms of probabilistic interpretation of plausibility. A new rule of combination of independent evidence is shown and its preservation of interpretation is…
The incompressibility method is an elementary yet powerful proof technique. It has been used successfully in many areas. To further demonstrate its power and elegance we exhibit new simple proofs using the incompressibility method.