Related papers: A generalization of Tanaka's formula
In this paper, we find a new recurrence formula fo the Euler zeta functions.
We derive an asymptotic formula which in some cases generalize Hadjicostas formula
This paper proposes a generalized ABC conjecture and assuming its validity settles a generalized version of Fermats last theorem.
We generalize Pappus chain theorem and give an analogue to this theorem.
We give a simple proof of a recently result concerning Hardy $q$-inequalities.
We prove several extensions of the Erdos-Fuchs theorem.
We define a Tanaka's equation on an oriented graph with two edges and two vertices. This graph will be embedded in the unit circle. Extending this equation to flows of kernels, we show that the laws of the flows of kernels $K$ solution of…
Several new applications of Katona's circle are given.
In this paper we prove the WALA conjecture.
A new generalization of the classical separate algebraicity theorem is suggested and proved.
We improve a result of Bennett concerning certain sequences involving sums of powers of positive integers.
For symmetric L\'evy processes, if the local times exist, the Tanaka formula has already constructed via the techniques in the potential theory by Salminen and Yor (2007). In this paper, we study the Tanaka formula for arbitrary strictly…
We give a new proof of Lucas' Theorem in elementary number theory.
Explicit formulas involving a generalized Ramanujan sum are derived. An analogue of the prime number theorem is obtained and equivalences of the Riemann hypothesis are shown. Finally, explicit formulas of Bartz are generalized.
We give a new proof of an important theorem by Nakazi using recent results by Sarason in his seminal paper on agebraic properties of truncated Toeplitz operators.
In this note a far extension of the Banach fixed point theorem is proved.
We obtained a new formula for $\pi$.
In this article we present a generalization of a Leibniz's geometrical theorem and an application of it.
In this paper, we will give a new proof for a known result of the mean square of Riemann zeta-function.
A proof of Sendov's conjecture is given.