The formula of Melzak for arbitrary polynomials
Khristo N. Boyadzhiev
TL;DR
This paper generalizes Melzak's binomial transform formula to apply to polynomials of any degree, broadening its mathematical utility and demonstrating various applications.
Contribution
It introduces a generalized Melzak formula for arbitrary degree polynomials, expanding the scope of the original binomial transform.
Findings
Extended Melzak formula valid for all polynomial degrees
Derived new applications of the generalized formula
Enhanced understanding of polynomial transformations
Abstract
We extend the well-known Melzak binomial transform formula to polynomials of any degree and show some applications.
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Taxonomy
TopicsMathematical functions and polynomials · Advanced Mathematical Identities · Mathematical Inequalities and Applications