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The term energy has an important physical meaning in physics and is an extremely useful concept. There are several forms energy defined in mathematics. In measure theory, let ...

Define I_n=(-1)^nint_0^infty(lnz)^ne^(-z)dz, (1) then I_n=(-1)^nGamma^((n))(1), (2) where Gamma^((n))(z) is the nth derivative of the gamma function. Particular values ...

_2F_1(a,b;c;z)=int_0^1(t^(b-1)(1-t)^(c-b-1))/((1-tz)^a)dt, (1) where _2F_1(a,b;c;z) is a hypergeometric function. The solution can be written using the Euler's ...

The inverse function of the Gudermannian y=gd^(-1)phi gives the vertical position y in the Mercator projection in terms of the latitude phi and may be defined for 0<=x<pi/2 ...

In toroidal coordinates, Laplace's equation becomes (1) Attempt separation of variables by plugging in the trial solution f(u,v,phi)=sqrt(coshu-cosv)U(u)V(v)Psi(psi), (2) ...

The continuous distribution with parameters m and b>0 having probability and distribution functions P(x) = (e^(-(x-m)/b))/(b[1+e^(-(x-m)/b)]^2) (1) D(x) = 1/(1+e^(-(x-m)/b)) ...

In 1979, Conway and Norton discovered an unexpected intimate connection between the monster group M and the j-function. The Fourier expansion of j(tau) is given by (1) (OEIS ...

The Nørlund polynomial (note that the spelling Nörlund also appears in various publications) is a name given by Carlitz (1960) and Adelberg (1997) to the polynomial ...

The parabolic cylinder differential equation is the second-order ordinary differential equation y^('')+(nu+1/2-1/4z^2)y=0 (1) whose solution is given by ...

A root-finding algorithm which assumes a function to be approximately linear in the region of interest. Each improvement is taken as the point where the approximating line ...