Transcendence of certain infinite products Original Research Article

We prove the transcendence results for the infinite product image, where Ek(x), Fk(x) are polynomials, α is an algebraic number, and rgreater-or-equal, slanted2 is an integer. As applications, we give necessary and sufficient conditions for transcendence of image and image, where Fn and Ln are Fibonacci numbers and Lucas numbers respectively, and {ak}kgreater-or-equal, slanted0 is a sequence of algebraic numbers with logdouble vertical barakdouble vertical bar=o(rk).