Entropies and the derivatives of some Heun functions
This short note contains a list of new results concerning the Rényi entropy, the Tsallis entropy, and the Heun functions associated with positive linear operators.
math.CA↗
arXiv subjects
Ioan Rasa
Publications and source records attributed to Ioan Rasa.
Special functions associated with positive linear operators
Many well-known positive linear operators (like Bernstein, Baskakov, Szász-Mirakjan) are constructed by using specific fundamental functions. The sums of the squared fundamental functions have been objects of study in some recent papers. We investigate the relationship between these sums and some special functions. Consequently, we get integral representations and upper bounds for the sums. Moreover, we show that they are solutions to suitable second order differential equations. In particular, we provide polynomial or rational solutions to some Heun equations.
math.CA↗