On a Recursion Formula and on Some Tauberian Theorems

Erdos, F eller, and Pollard [2] pro ved that if the greatest common divi or of the k's with c,,>O is 1, then , Other theorems of the same type as theorem 1 were proved by T . Kaluza [4] . Assuming (1) , he showed for instance, that j (2) > 0, j (n l )j (n + 1) > p(n ) (n = 2,3, . .. ) imply that the c's are positive. Furthermore, he proved that j (I ),j(2), ... is a moment equence if, and only if, Cl, C2, Ca, • •• is a moment sequence. (H ere Cl, C2, Ca, • • • is call ed a moment equence whenever it is of the form an= So '" undx (u), where x(u ) is nondecrea ing and