During his time in Freiburg, Lindemann devised his proof that π is a transcendental number (see Lindemann–Weierstrass theorem).
'Optimization: Insights and Applications', Jan Brinkhuis and Vladimir Tikhomirov: 2005, Princeton University Press
That such a function can be constructed follows from the Weierstrass theorem and Mittag-Leffler theorem.
Liouville's theorem | Karl Weierstrass | Chinese remainder theorem | Shannon–Hartley theorem | Quillen–Suslin theorem | Nyquist–Shannon sampling theorem | Hahn–Banach theorem | Fermat's Last Theorem | Buckingham π theorem | Thue–Siegel–Roth theorem | Szemerédi's theorem | Schottky's theorem | Riemann-Roch theorem | Pythagorean theorem | Nash embedding theorem | Müntz–Szász theorem | Malgrange–Ehrenpreis theorem | Kleene fixed-point theorem | Kakutani fixed-point theorem | Gauss–Bonnet theorem | Doob's martingale convergence theorem | Dirichlet's theorem on arithmetic progressions | Denjoy theorem | Birch's theorem | Wilkie's theorem | Wick's theorem | Whitney extension theorem | Weierstrass theorem | Weierstrass–Erdmann condition | Wedderburn's little theorem |