arXiv subjects

Narinder Kumar Wadhawan

Publications and source records attributed to Narinder Kumar Wadhawan.

5 recordsLinked to original sources

arXiv2025

Representation Of Integers By Sum Of Three Cubes, A New Approach Based On Seed Equation

We have proved in this paper that numbers can be expressed in algebraic form using one variable and two real rational quantities and thus sum of three cubes can also be expressed in algebraic form as a cubic polynomial. Using skeletal or seed equation, the polynomial can be transformed into a quadratic equation. A seed equation denotes a simple equation that represents a given integer as sum of three cubes including 0, for example, a seed equation for integer 2 is 1 cubed plus 1 cubed plus 0 cubed. Resultant quadratic equation can further be transformed into a linear equation which yields value of the variable and substitution of the value of the variable into the algebraic form of numbers results in the required solution. Notwithstanding, finding a single set of three cubes, we have found, using this approach, multiple sets of cubes. We have also given parametrisation for such cubes. Cases, where it is difficult or not possible to determine a seed equation, alternate method has been provided. Methods used are unattempted, innovative and easily comprehensible.

math.GM↗

arXiv2025

Approximation Of Logarithm, Factorial And Euler Mascheroni Constant Using Odd Harmonic Series

We have proved in this paper that natural logarithm of consecutive number ratio, x/(x-1) approximates to 2/(2x - 1) where x is a real number except 1. Using this relation, we, then proved, x approximates to double the sum of odd harmonic series having first and last terms 1/3 and 1/(2x - 1) respectively. Thereafter, not limiting to consecutive number ratios, we extended its applicability to all the real numbers. Based on these relations, we, then derived a formula for approximating the value of Factorial x. We could also approximate the value of Euler-Mascheroni constant. In these derivations, we used only and only elementary functions, thus this paper is easily comprehensible to students and scholars.

math.NT↗

arXiv2025

Scientific Calculator With The Aid Of Geometry And Based Upon It, A Mechanical Calculator

Scientific calculations involving multiplication, division, exponents, inverse exponents of real numbers, geometric mean, reciprocal, Euler number, logarithm, and antilogarithm are generally carried out using battery operated electronic calculators. In this paper, geometric methods employing properties of similar right angled triangles have been devised for performing error free scientific calculations without the use of batteries. Based on this method, a mechanical analogue calculator has also been designed. A right-angled triangle with one perpendicular side of unit length is drawn, and from the vertex of the right angle, a perpendicular is drawn onto the hypotenuse. From the point of intersection of this perpendicular with the hypotenuse, another perpendicular is drawn to the base, and this process is continued until n perpendiculars are drawn. The resultant figure is a right angled triangle containing n similar triangles. Using properties of similar triangles, it is found that the lengths of the first, second, third so on till last perpendicular form a geometric series. If the length of the nth perpendicular is equated to a given real positive quantity less than one, and the base angle is adjusted, then the length of the first perpendicular represents the nth root of the given quantity. If the given quantity is greater than one, its reciprocal is equated to the length of the nth perpendicular, and the reciprocal of the first perpendicular gives the nth root. In this manner, several scientific calculations can be performed using geometric techniques.

math.NA↗

arXiv2025

Numerical Approximation In Real Domain Of Special Function Of Product Of A Variable And Its Double Exponential

Purpose of writing this paper is to solve a transcendental function containing a product of a variable and its double exponential by a unique method of approximation. If the value of the said product is given, then its inverse function is approximated by use of linear expression in place of natural logarithm of a positive real quantity and, that transforms the function to a quadratic equation. Roots of the equation are, then used for solving the function. For precise approximation, the process is iterated a number of times and more the number of iterations, more precise will be the approximation. To prove truthfulness of the formulae derived, a number of examples are given in tabular form.

math.NA↗

arXiv2025

Numerical Approximation of Lambert W Function For Real Values By Unique Method of Quadratic Approximation

This paper introduces a new numerical method for approximating the Lambert W function in the real domain. The method transforms the function into a simpler form that allows iterative refinement of an initial guess. Two iterative strategies are proposed for positive inputs, and the method is extended to handle negative inputs within a defined range. Unlike standard methods, this approach works for both branches without restrictive initial assumptions. Examples and software demonstrate the accuracy and flexibility of the method.

math.NA↗