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
Related Articles
- EP ID EP190298
- DOI -
- Views 93
- Downloads 0
Recurrence formula, differential compound and differential equations for Laguerre polynomials
Introduction and aim: The paper presents a recurrence formula, some differential compounds and differential equation for Laguerre polynomials. The aim of the discussion was to give some proofs of presented dependences. M...
Rola polimorfizmów genów MCPH1 i ASPM/MCPH5 w rozwoju mózgowia
Wstęp i cele: Adaptacja ewolucyjna anatomii mózgowia u człowieka rozumnego właściwego pozostaje w zależności z genetycznymi regulatorami rozwoju objętości mózgowia. Do puli genów ewolucyjnych wykazujących zaangażowanie w...
Związek rekurencyjny oraz zależności i równanie różniczkowe dla wielomianów Legendre'a
W pracy przedstawiono związek rekurencyjny, zależności różniczkowe i równanie różniczkowe dla wielomianów Legendre’a. Celem rozważań było przeprowadzenie dowodów omawianych własności. Materiał i metody: Materiał stanowił...
Anatomical disorders of genitourinary system in children with sirenomelia in diagnostic imaging
Introduction and aim: Sirenomelia sequence is a rare congenital malformation characterized with a single midline lower limb. Material and methods: Information comes from available literature sources that were reviewed. T...
Organization of work safety at the electrical equipment
Introduction and aim: The paper presents the problem of accident rate at work with taking into consideration the particular safety at electrical equipment. They point out, that the main cause of accidents at work is the...