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The cosine function cosx is one of the basic functions encountered in trigonometry (the others being the cosecant, cotangent, secant, sine, and tangent). Let theta be an ...

The function frac(x) giving the fractional (noninteger) part of a real number x. The symbol {x} is sometimes used instead of frac(x) (Graham et al. 1994, p. 70; Havil 2003, ...

In a 1847 talk to the Académie des Sciences in Paris, Gabriel Lamé (1795-1870) claimed to have proven Fermat's last theorem. However, Joseph Liouville immediately pointed out ...

The plots above show the values of the function obtained by taking the natural logarithm of the gamma function, lnGamma(z). Note that this introduces complicated branch cut ...

The natural logarithm lnx is the logarithm having base e, where e=2.718281828.... (1) This function can be defined lnx=int_1^x(dt)/t (2) for x>0. This definition means that e ...

A special function mostly commonly denoted psi_n(z), psi^((n))(z), or F_n(z-1) which is given by the (n+1)st derivative of the logarithm of the gamma function Gamma(z) (or, ...

Two integers are relatively prime if they share no common positive factors (divisors) except 1. Using the notation (m,n) to denote the greatest common divisor, two integers m ...

secz is the trigonometric function defined by secz = 1/(cosz) (1) = 2/(e^(iz)+e^(-iz)), (2) where cosz is the cosine. The secant is implemented in the Wolfram Language as ...

A sultan has granted a commoner a chance to marry one of his n daughters. The commoner will be presented with the daughters one at a time and, when each daughter is ...

There are many unsolved problems in mathematics. Some prominent outstanding unsolved problems (as well as some which are not necessarily so well known) include 1. The ...