On the roots of the Rogers-Ramanujan function

PABLO ANDRES PANZONE

ROCKY MOUNTAIN JOURNAL OF MATHEMATICS

ROCKY MT MATH CONSORTIUM

Año: 2018 p. 1 - 6

0035-7596

Abstract. We give simple proofs of the fact that for certain parametersthe roots of the generalized Rogers-Ramanujan function are irrational num-bers and, for example, that at least one of the following two numbers is ir-rational:P1n=1FnmnQn􀀀1i=0 (k+i);P1n=1FnmnQn􀀀1i=0 (k+i+1)where Fn+2 =Fn+1 + Fn, F0 = 0; F1 = 1 (the Fibonacci sequence), m is a natural num-ber > 1+p52 and (k) is any function taking positive integer values such thatlim supk!1 (k) = 1.