اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدNew Gelfond-Type Transcendental Numbers
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It is well known that value at a non-zero algebraic number of each of the functions $e^{x}, ln x, sin x, cos x, tan x, csc x, sec x, cot x, sinh x,$ $ cosh x,$ $ tanh x,$ and $coth x$ is transcendental number (see Theorem 9.11 of cite{N}). In the work, we show that for any one of the above mentioned functions, $f(x)$, and for a polynomial $g(x)$ with rational coefficients the zero, if any, of the equation $f(x)=g(x)$ is a transcendental number. We also show that if $f(x)$ and $g(x)$ are polynomials with rational coefficients, then a zero of the equation $e^{f(x)}=g(x)$ is a transcendental number. Finally we show that the existence of an abelian group whose non-zero elements are transcendental numbers.
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