Gelfond's constantIn mathematics, Gelfond's constant, named after Aleksandr Gelfond, is e^π, that is, e raised to the power pi. Like both e and pi, this constant is a transcendental number. This was first established by Gelfond and may now be considered as an application of the Gelfond–Schneider theorem, noting that where i is the imaginary unit. Since −i is algebraic but not rational, e^π is transcendental. The constant was mentioned in Hilbert's seventh problem. A related constant is 2^, known as the Gelfond–Schneider constant.
Ferdinand von LindemannCarl Louis Ferdinand von Lindemann (12 April 1852 – 6 March 1939) was a German mathematician, noted for his proof, published in 1882, that pi (pi) is a transcendental number, meaning it is not a root of any polynomial with rational coefficients. Lindemann was born in Hanover, the capital of the Kingdom of Hanover. His father, Ferdinand Lindemann, taught modern languages at a Gymnasium in Hanover. His mother, Emilie Crusius, was the daughter of the Gymnasium's headmaster. The family later moved to Schwerin, where young Ferdinand attended school.
Champernowne constantIn mathematics, the Champernowne constant C10 is a transcendental real constant whose decimal expansion has important properties. It is named after economist and mathematician D. G. Champernowne, who published it as an undergraduate in 1933. For base 10, the number is defined by concatenating representations of successive integers: C10 = 0.12345678910111213141516... . Champernowne constants can also be constructed in other bases, similarly, for example: C2 = 0.11011100101110111... 2 C3 = 0.12101112202122..
Apéry's theoremIn mathematics, Apéry's theorem is a result in number theory that states the Apéry's constant ζ(3) is irrational. That is, the number cannot be written as a fraction where p and q are integers. The theorem is named after Roger Apéry. The special values of the Riemann zeta function at even integers () can be shown in terms of Bernoulli numbers to be irrational, while it remains open whether the function's values are in general rational or not at the odd integers () (though they are conjectured to be irrational).
Hurwitz zeta functionIn mathematics, the Hurwitz zeta function is one of the many zeta functions. It is formally defined for complex variables s with Re(s) > 1 and a ≠ 0, −1, −2, ... by This series is absolutely convergent for the given values of s and a and can be extended to a meromorphic function defined for all s ≠ 1. The Riemann zeta function is ζ(s,1). The Hurwitz zeta function is named after Adolf Hurwitz, who introduced it in 1882. The Hurwitz zeta function has an integral representation for and (This integral can be viewed as a Mellin transform.
Square root of 3The square root of 3 is the positive real number that, when multiplied by itself, gives the number 3. It is denoted mathematically as or . It is more precisely called the principal square root of 3 to distinguish it from the negative number with the same property. The square root of 3 is an irrational number. It is also known as Theodorus' constant, after Theodorus of Cyrene, who proved its irrationality. its numerical value in decimal notation had been computed to at least ten billion digits.
