Related papers: A generalization of Tanaka's formula

By changing variables in a suitable way and using dominated convergence methods, this note gives a short proof of Stirling's formula and its refinement.

We present a simple inductive proof of the Lagrange Inversion Formula.

We prove a new theorem on additive Levy processes and show that this theorem implies several proved theorems and a hard conjectured theorem.

We put a new conjecture on primes from the point of view of its binary expansions and make a step towards justification.

In a present note we give a new proof of Etingof-Kazhdan quantization theorem.

We present a relative form of the Toponogov comparison theorem.

In this paper we will give a proof of a certain summation formula for Gamma functions utilizing Gegenbauer polynomials.

We show a sum formula of certain multiple L-values conjectured by Essouabri-Matsumoto-Tsumura, which generalizes the sum formula of multiple zeta-values. The proof relies on the method of partial fraction decomposition.

In this note, we make a correction of the imaginary transformation formula of Chan and Liu's circular formula of theta functions. We also get the imaginary transformation formulaes for a type of generalized cubic theta functions.

We prove two conjectures posed in 2016 concerning a generalization of the Sawayama-Th\'ebault Theorem and the Sawayama Lemma. We show that this generalized statement can be viewed in Laguerre geometry, which provides a natural framework for…

This should be the final version of this paper. Numberous minor improvements have been made to the manuscript, one argument has been corrected, and an appendix has been added.

We introduce the concept of shifting distance functions, and we establish a new fixed point theorem which generalizes the Banach contraction principle. An example is provided to illustrate our result.

We prove some extensions of Andrews inequality.

The sum formula is one of the most well-known relations among multiple zeta values. This paper proves a conjecture of Kaneko predicting that an analogous formula holds for finite multiple zeta values.

We give effective bounds for the uniformity of the Iitaka fibration. These bounds follow from an effective theorem on the birationality of some adjoint linear series. In particular we derive an effective version of the main theorem in [17].

An infinite dimensional algebra, which is useful for deriving exact solutions of the generalized pairing problem, is introduced. A formalism for diagonalizing the corresponding Hamiltonian is also proposed. The theory is illustrated with…

We establish a new lower bound for Mathieu's series and present a new derivation of its expansions in terms of Riemann Zeta functions.

In this note we provide a simple formula of general term of recurrent sequence.

We derive a new generalization of the nonlinear variational wave equation. We prove existence of local, smooth solutions for this system. As a limiting case, we recover the nonlinear variational wave equation.

We give a new proof of Brooks' theorem that immediately implies a strengthening of Brooks' theorem, known as Catlin's theorem.