Europe PMC

On Multi-Order Logarithmic Polynomials and their Explicit Formulas, Recurrence Relations, and Inequalities

In the paper, the author introduces the notions "multi-order logarithmic numbers" and "multi-order logarithmic polynomials", establishes an explicit formula, an identity, and two recurrence relations ...
Scientific Research Publishing

Horiguchi, S. (2011) General Recurrence Formula Obtained from the Murase Yoshimasu’s Recurrence Formulas and Newton’s Method. RIMS, 1739, 234-244. (in Japanese)

ABSTRACT: In 1673, Yoshimasu Murase made a cubic equation to obtain the thickness of a hearth. He introduced two kinds of recurrence formulas of square and the deformation (Ref.[1]). We find that the ...
IEEE

Exactly initialized recursive least squares

Abstract: In this paper, we present three order-recursive formulas for the Moore-Penrose pseudoinverses of matrices which are the improved and extended Greville formulas (1960). These new versions not ...
Scientific Research Publishing

Xu, C.N. (2013) Operator Proof of Recurrence Formula of Stirling Number of the First Kind. Journal of Inner Mongolia University for the Nationalities (Natural Sciences), 4, 384 ...

ABSTRACT: This article investigated the idea of Shape of numbers and introduced new operators. The idea divides all products of k distinct integers in [1, n - 1] into 2K-1 catalogs and derives the ...
GitHub

Recursive Field: Mathematical Formulas

This repository contains mathematical models inspired by the “Recursive Field” scientific math song. The song describes a pattern reminiscent of phyllotaxis (the arrangement of leaves or seeds) where ...