On the Construction of a Family of Transcendental Valued Infinite Products
نویسنده
چکیده
In recent time there has been much progress made on the problem of determining sufficiency conditions for a positive rational termed series to converge to either an irrational or transcendental number (see [1], [4], [6] and the references cited therein). Surprisingly, in comparison, very little attention has been paid to finding such sufficiency conditions in the case of infinite products. One such sufficiency condition is attributable to Cantor (see [3]) however some generalisations of this condition have also been obtained in [8]. Cantor, in particular, proved that if {an} is a sequence of positive integers such that an+1 > an then the infinite product ∞ ∏
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