Search Results for ""

Infinite series of various simple functions of the logarithm include sum_(k=1)^^^inftylnk = 1/2ln(2pi) (1) sum_(k=1)^^^infty(-1)^klnk = 1/2ln(1/2pi) (2) ...

Oloa (2010, pers. comm., Jan. 20, 2010) has considered the following integrals containing nested radicals of 1/2 plus terms in theta^2 and ln^2costheta: R_n^- = (1) R_n^+ = ...

The Rayleigh functions sigma_n(nu) for n=1, 2, ..., are defined as sigma_n(nu)=sum_(k=1)^inftyj_(nu,k)^(-2n), where +/-j_(nu,k) are the zeros of the Bessel function of the ...

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 condition in numerical equation solving which states that, given a space discretization, a time step bigger than some computable quantity should not be taken. The condition ...

E. Pegg Jr. (pers. comm., Nov. 8, 2004) found an approximation to Apéry's constant zeta(3) given by zeta(3) approx 10+zeta(16)-sqrt(96), (1) which is good to 6 digits. M. ...

The Lambert W-function, also called the omega function, is the inverse function of f(W)=We^W. (1) The plot above shows the function along the real axis. The principal value ...

A formula which transforms a given coordinate system by rotating it through a counterclockwise angle Phi about an axis n^^. Referring to the above figure (Goldstein 1980), ...

The Catalan numbers on nonnegative integers n are a set of numbers that arise in tree enumeration problems of the type, "In how many ways can a regular n-gon be divided into ...

A series is said to be conditionally convergent iff it is convergent, the series of its positive terms diverges to positive infinity, and the series of its negative terms ...