Recurrence formula, differentia compound and differentia equations for Hermite polynomials

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Recurrence formula, differentia compound and differentia equations for Hermite polynomials

Journal Title: Problemy Nauk Stosowanych - Year 2016, Vol 4, Issue

Abstract

Introduction and aim: The paper presents a recurrence formula, some differential compounds and differential equation for Hermite polynomials. The aim of the discussion was to give some proofs of presented dependences. Material and methods: Selected material based on a recurrence formula, some differential compounds and differential equation has been obtained from the right literature. In presented proofs of theorems was used a deduction method. Results: Has been shown some proof of the theorem of the generating function for Hermite polynomials. It has been done the proof of recurrence formula between Hermite polynomials, some proof of differential compound and two differential equations for Hermite polynomials. Conclusion: The derivative of Hermite polynomial expressed by Hermite polynomials can be determined from the equation H’n(z) = 2nHn-1(z) for n = 1, 2, 3, ... .

Authors and Affiliations

Andrzej Antoni Czajkowski, Paweł Ignaczak, Roman Udała

Keywords

Analiza historyczno-porównawcza języka matematyki w zakresie trygonometrii na podstawie podręcznika Stanisława Przystańskiego „Trygonometrya prostokreślna” z 1859 roku

Wstęp i cel: Porównanie językowo-historyczne w naukach matematycznych ma na celu ujawnienie zmian w sposobie myślenia ówczesnych i dzisiejszych matematyków oraz skutków tych zmian. Analiza ukazuje jak różne podejścia do...

EP ID EP190298
DOI -
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