Results 1 to 10 of about 138 (96)

An Automatic Proof of Euler's Formula [PDF]

Computer Science Journal of Moldova, 2005
In this information age, everything is digitalized. The encoding of functions and the automatic proof of functions are important. This paper will discuss the automatic calculation for Taylor expansion coefficients, as an example, it can be applied to
Jun Zhang
doaj   +3 more sources

Some Properties of Euler’s Function and of the Function τ and Their Generalizations in Algebraic Number Fields

Mathematics, 2021
In this paper, we find some inequalities which involve Euler’s function, extended Euler’s function, the function τ, and the generalized function τ in algebraic number fields.
Nicuşor Minculete, Diana Savin
doaj   +1 more source

Applications of neutrosophic complex numbers in triangles [PDF]

Neutrosophic Sets and Systems, 2023
It may be difficult for researchers to memorize or remember the trigonometric ratios of any neutrosophic angle, and this is what prompted us to activate the role of the neutrosophic complex numbers for that.
Yaser Ahmad Alhasan, Iqbal Ahmed Musa, Isra Abdalhleem Hassan Ali   +2 more
doaj   +1 more source

The Derivation of the Riemann Analytic Continuation Formula from the Euler’s Quadratic Equation

Journal of Nigerian Society of Physical Sciences, 2022
The analysis of the derivation of the Riemann Analytic Continuation Formula from Euler’s Quadratic Equation is presented in this paper. The connections between the roots of Euler’s quadratic equation and the Analytic Continuation Formula of the Riemann ...
Opeyemi O. Enoch, Adejimi A. Adeniji, Lukman O. Salaudeen   +2 more
doaj   +1 more source

Unification Theories: Rings, Boolean Algebras and Yang–Baxter Systems

Axioms, 2023
This paper continues a series of papers on unification constructions. After a short discussion on the Euler’s relation, we introduce a matrix version of the Euler’s relation, E I π+U=O.
Florin F. Nichita
doaj   +1 more source

A new Euler's formula for DNA polyhedra. [PDF]

PLoS ONE, 2011
DNA polyhedra are cage-like architectures based on interlocked and interlinked DNA strands. We propose a formula which unites the basic features of these entangled structures.
Guang Hu, Wen-Yuan Qiu, Arnout Ceulemans
doaj   +1 more source

K-regular decomposable incidence structure of maximum degree [PDF]

Mathematica Moravica, 2023
This paper discusses incidence structures and their rank. The aim of this paper is to prove that there exists a regular decomposable incidence structure J = (P, B) of maximum degree depending on the size of the set and a predetermined rank.
Stošović Dejan, Katić Anita, Galić Dario   +2 more
doaj   +1 more source

Some Numerical Significance of the Riemann Zeta Function

Recent Advances in Natural Sciences, 2023
In this paper, the Riemann analytic continuation formula (RACF) is derived from Euler’s quadratic equation. A nonlinear function and a polynomial function that were required in the derivation were also obtained.
Opeyemi O. Enoch, Lukman O. Salaudeen
doaj   +1 more source

Some Results on the Extended Hypergeometric Matrix Functions and Related Functions

Journal of Mathematics, 2021
In this article, we discuss certain properties for generalized gamma and Euler’s beta matrix functions and the generalized hypergeometric matrix functions.
Mohamed Abdalla, Sahar Ahmed Idris, Ibrahim Mekawy   +2 more
doaj   +1 more source

General dual Euler-Simpson formulae [PDF]

Journal of Mathematical Inequalities, 2008
We consider a general dual Simpson formulae, using some Euler-type identities. A number of inequalities, for functions whose derivatives are either functions of bounded variation or Lipschitzian functions or $R$-integrable functions, are proved.
Pečarić, Josip, Vukelić, Ana
openaire   +4 more sources