Related papers: Origin of the numerals, Al biruni testimony
These notes explore three amazing formulas proved by Abel in his 1826 Paris memoir on what we now call Abelian integrals. We discuss the first two formulas from the point of view of symbolic computation and explain their connection to…
Handwritten numeral recognition is in general a benchmark problem of Pattern Recognition and Artificial Intelligence. Compared to the problem of printed numeral recognition, the problem of handwritten numeral recognition is compounded due…
In this paper, we give some recurrence formula and new and interesting identities for the poly-Bernoulli numbers and polynomials which are derived from umbral calculus.
Handwritten digit or numeral recognition is one of the classical issues in the area of pattern recognition and has seen tremendous advancement because of the recent wide availability of computing resources. Plentiful works have already done…
In this work initial numbers and repunit numbers have been studied. All numbers have been considered in a decimal notation. The problem of simplicity of initial numbers has been studied. Interesting properties of numbers repunit are proved:…
Prime numbers are fascinating by the way they appear in the set of natural numbers. Despite several results enlighting us about their repartition, the set of prime numbers is often informally qualified as misterious. In the present paper,…
We first establish the result that the Narayana polynomials can be represented as the integrals of the Legendre polynomials. Then we represent the Catalan numbers in terms of the Narayana polynomials by three different identities. We give…
It is widely believed that the advance of science in the Islamic world after the mid-fifteenth century A.D. suffered a decline. For the purpose of examining this belief, a manuscript by Qasim ali al-Qayini (ca. A.D.1685) was chosen based on…
The classical sequence of Bernoulli numbers is known to the the sequence of moments of a family of orthogonal polynomials. Some similar statements are obtained for another sequence of rational numbers, which is similar in many ways to the…
In this paper, we highlight the influence of Arab/Islamic civilization in the field of the history of astronomy on European historians. We also aim to elucidate the stance of Orientalists toward the study of Arab sciences and to clarify…
We show that many ancient Indian mythological legends are really allegorical depictions of astronomical and other physical phenomena of which the composers had a good idea. This detail enables us to also use techniques of astronomical…
Despite ongoing calls for inclusive and culturally responsive pedagogy in computing education, the teaching of algorithms remains largely decontextualized. Foundational computer science courses often present algorithmic thinking as purely…
Mathematicians have long been fascinated by the resolution of algebraic and Diophantine equations in search of integer or rational solutions. This article presents a list of thirty-three open problems in number theory, posed in the 13th…
The earliest origins of mathematics in the Indian subcontinent is generally dated around 800-500 BCE when the {\em Sulbasutras} are thought to have been written. In this article we suggest that mathematical thinking in South Asia, in…
Throughout more than two millennia many formulas have been obtained, some of them beautiful, to calculate the number pi. Among them, we can find series, infinite products, expansions as continued fractions and expansions using radicals.…
We report the emergence of a striking new phenomenon in arithmetic, which we call murmurations. First observed experimentally through averages over large arithmetic datasets, murmurations can be detected and analyzed using standard…
In Babylonian mathematics two Sumerian words of fractions occur, which were originally used in non-mathematical texts. They are igi-n-g\'al "the reciprocal of (the number) n", which is often abbreviated to igi-n, and igi-te-en whose meaning…
We provide textual evidence on divisibility and primality in the ancient Vedic texts of India. Concern with divisibility becomes clear from the listing of all the fifteen pairs of divisors of the number 720. The total number of pairs of…
We derive an identity involving Horadam numbers. Numerous new identities as well as those found in the existing literature are subsumed in this single identity.
In this paper, we introduce multi-Lah numbers and multi-Stirling numbers of the first kind and recall multi-Bernoulli numbers, all of whose generating functions are given with the help of multiple logarithm. The aim of this paper is to…