lpetrich
Contributor
Inverse trigonometric and hyperbolic functions are transcendental for their argument algebraic and nonzero -- a consequence of the Lindemann-Weierstrass theorem
arctan(x)/pi is transcendental for x rational -- a consequence of the Gelfond-Schneider theorem
Transcendentality of zeros of higher dereivatives of functions involving Bessel functions - Lorch - 1995 - International Journal of Mathematics and Mathematical Sciences - Wiley Online Library
Bessel functions J(n,x), their first derivatives J'(n,x) = (d/dx)J(n,x), and one divided by the other, J'(n,x)/J(n,x), are all transcendental for n rational and x algebraic and nonzero.
All nonzero roots of J(n,x) and J'(n,x) are transcendental if n is rational.
arctan(x)/pi is transcendental for x rational -- a consequence of the Gelfond-Schneider theorem
Transcendentality of zeros of higher dereivatives of functions involving Bessel functions - Lorch - 1995 - International Journal of Mathematics and Mathematical Sciences - Wiley Online Library
Bessel functions J(n,x), their first derivatives J'(n,x) = (d/dx)J(n,x), and one divided by the other, J'(n,x)/J(n,x), are all transcendental for n rational and x algebraic and nonzero.
All nonzero roots of J(n,x) and J'(n,x) are transcendental if n is rational.