General Mathematics
Taylor's theorem (and its variants) is widely used in several areas of mathematical analysis, including numerical analysis, functional analysis, and partial differential equations. This article explains how Taylor's theorem in its most…
While there is not much publications, about degree sixteen Diophantine equation we do have an identity given by Ramanujan (ref. #1). Also on the internet even though there are numerical solutions to degree sixteen for eg. (16-7-24) equation…
In this article, a new class of the entire function of order one, expressed by the series and product representations with the real positive coefficients and complex zeros, is investigated for the first time. The entire function on the…
In this article we propose a new class of the even entire function connected with the product and series with the real coefficients. We address a sufficient condition for all real zeros for it. As a typical example, we give an answer to the…
In this manuscript we provide a new polynomial pattern. This pattern allows to find a polynomial expansion of the form \[x^{2m+1} = \sum_{k=1}^{x}\sum_{r=0}^{m} \mathbf{A}_{m,r} k^r (x-k)^r,\] where $x,m\in\mathbb{N}$ and $\mathbf{A}_{m,r}$…
This paper mainly investigates the distributive laws between extended nullnorms and uninorms on fuzzy truth values under the condition that the nullnorm is conditionally distributive over the uninorm. It presents the distributive laws…
In this paper we use a contour integral method to derive a generating function in the form of a double series involving the product of two Chebyshev polynomials over generalized independent indices expressed in terms of the incomplete gamma…
I show here that there are three different kinds of iterations for the reduced Collatz algorithm; depending on whether the root of the number is odd or even. There is only one kind of iteration if the root is odd and two kinds if the root…
For the N>=2 dimensional incompressible Naver-Stokes Equation, We have got its solution as a power series of time t, in which the coefficients are all known functions determined only by the initial velocity v0. We also prove that the…
Classical geometric fractals - Cantor set and Sierpinski continua - are presented in the manual as set-theoretic objects.
All intuitionistic fuzzy TOPSIS methods contain two key elements: (1) the order structure, which can affect the choices of positive ideal-points and negative ideal-points, and construction of admissible distance/similarity measures; (2) the…
Previously we have proposed a new method of transforming quotients into integer reciprocals in the Machin-like formulas for $\pi$. As a further development, here we show how to generate a multi-term Machin-like formula for $\pi$ with a…
Multiplication by the pseudoscalar $\mathbf{I}$ has been traditionally used in geometric algebra to perform non-metric operations such as calculating coordinates and the regressive product. In algebras with degenerate metrics, such as…
In this article, we aim at obtaining the analytical expression ({\bf not previously found and recorded in the literature}) for the exact curved surface area of a hyperboloid of one sheet in terms of Srivastava-Daoust triple hypergeometric…
Differential operators usually result in derivatives expressed as a ratio of differentials. For all but the simplest derivatives, these ratios are typically not algebraically manipulable, but must be held together as a unit in order to…
The Ulam spiral inspired us to calculate and present Lissajous curves where the orthogonally added functions are a finite sum of sinus and cosines functions with consecutive prime number frequencies.
Recently we have reported a new method of rational approximation of the sinc function obtained by sampling and the Fourier transforms. However, this method requires a trigonometric multiplier that originates from shifting property of the…
Our present investigation is motivated essentially by several interesting applications of generalized hypergeometric functions of one, two and more variables. The hypergeometric functions are potentially useful and have widespread…
ABSTRACT. The triple Shehu transform, a new generalisation of the triple Laplace transforms and triple Sumudu transform, has recently been introduced. The triple Shehu transform formulas for fractional Caputo operators were obtained in this…
This paper presents new formulary solutions for quantic polynomial equations in general forms, where we present five solutions for any fifth degree polynomial equation with real coefficients, and thereby having the possibility to calculate…