Lothar Berg, Manfred Krüppel
Recursions for the Solution of an Integral-Functional Equation
The paper is published: Rostocker Mathematisches Kolloquium, Rostock. Math. Kolloq. 58, 101-122(2004)

MSC:

45D05 Volterra integral equations, See also {34A12}

39A10 Difference equations, See also {33Dxx}

26C05 Polynomials: analytic properties, etc., See also {12Dxx,

05C90 Applications

Abstract: In this paper, we continue our considerations
in \cite{kru-bk1,kru-bk2,kru-bk3} about
a homogeneous integral-functional equation with a parameter
$a>1$. Here we assume that $a\ge2$, disregarding some explicitly
mentioned cases where $a$ can be smaller than 2.
We derive new recursions which allow
to calculate the solution and its derivatives effectively,
and which contain formulas of R. Schnabl \cite{kru-sch}
and W. Volk \cite{kru-vo1} as special cases for $a=2$.
Keywords: Integral-functional equation, generating functions, Cantor sets, relations containing polynomials, recursions, directed graphs.