Algebraic independence of reciprocal sums of certain Fibonacci-type   numbers
  The paper studies algebraic independence of certain reciprocal sums of Fibonacci and Lucas sequences. Also more general binary recurrences are considered. The main tool is Mahler's method reducing the investigation of the algebraic independence of function values to the one of functions if these satisfy certain types of functional equations. 
Peter Bundschuh and Keijo V\"a\"an\"anen
math.NT