Related papers: A generalization of Tanaka's formula

We obtain some results related to Romanoff's theorem.

In this paper we give a generalization of Iseki's formula and use it to prove the transformation law of $\theta_1(z, \tau)$.

We generalize Romanoff's theorem. Also, we obtain a result on sums related to Euler's totient function.

We give a generalization of Fujisawa's theorem in [F]. Our proof of the generalized theorem is purely algebraic and it is simpler than his proof.

In this paper we study a group theoretical generalization of the well-known Gauss's formula that uses the generalized Euler's totient function introduced in [11].

A generalization of the law of total covariance is presented and proved.

We present a generalization of a formula of higher order derivatives and give a short proof.

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

In this paper some new ways of generalizing perfect numbers are investigated, numerical results are presented and some conjectures are established.

We prove an improved form of an expectation of Polya and discuss several related questions

We analyze a system of linear algebraic equations whose solutions lead to a proof of a generalization of Boole's formula. In particular, our approach provides an elementary and short alternative to Katsuura's proof of this generalization.

We prove a generalization of Istvan F\'ary's celebrated theorem to higher dimension.

In this note, we prove a quantization formula for singular reductions. The main result is obtained as a simple application of an extended quantization formula proved in [TZ2].

We prove some generalizations of the sum formula for multiple zeta values by using Hiroyuki Ochiai's method of proving the sum formula.

We prove the theorems which are equivalent to the Roland's results such that a new form of them allows to consider some generalizations. In particular, we give generators of primes more than a fixed prime.

We introduce a new criterion which if satisfied implies the Riemann hypothesis.

We provide new sufficient conditions under which Ryser's conjecture holds.

We generalize Jacod's condition and introduce a new type sufficient condition for the uniform integrability of the general stochastic exponential.

In this paper, by using analytical methods we obtain a generalization of the famous Kodaira embedding theorem.

The paper contains an interesting generalization of the classical Taylor expansion formula and four applications