Cnoidal wave is the wave height, "λ" is the wavelength, "c" is the phase speed and "η" is the trough elevation. Further cn is one of the Jacobi elliptic functions and "K"("m") is the complete elliptic integral of the first kind; both are dependent on the elliptic parameter "m". The latter, "m", determines the shape of the cnoidal wave. For "m" equal to zero the cnoidal wave becomes a cosine function, while for values close to one the cnoidal wave gets peaked crests and (very) flat troughs. For values of "m" less than 0.95, the cnoidal function can be approximated with trigonometric
Champernowne constant Champernowne constant In mathematics, the Champernowne constant 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: Champernowne constants can also be constructed in other bases, similarly, for example: The Champernowne constants can be expressed exactly as infinite series: where formula_2 ceiling(formula_3), formula_4 in base 10, formula_5 and formula_6 is the base of the constant. A slightly different expression is given by Eric W. Weisstein (MathWorld): where formula_8