  Many well-known positive linear operators (like Bernstein, Baskakov,
Sz\'{a}sz-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.
