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A "weird number" is a number that is abundant (i.e., the sum of proper divisors is greater than the number) without being pseudoperfect (i.e., no subset of the proper ...

The inverse cotangent is the multivalued function cot^(-1)z (Zwillinger 1995, p. 465), also denoted arccotz (Abramowitz and Stegun 1972, p. 79; Harris and Stocker 1998, p. ...

Define q=e^(2piitau) (cf. the usual nome), where tau is in the upper half-plane. Then the modular discriminant is defined by ...

A branch point of an analytic function is a point in the complex plane whose complex argument can be mapped from a single point in the domain to multiple points in the range. ...

_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 ...

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) ...

An integral transform which is often written as an ordinary Laplace transform involving the delta function. The Laplace transform and Dirichlet series are special cases of ...

An even Mathieu function ce_r(z,q) with characteristic value a_r.

A mathematical relationship transforming a function f(x) to the form f(x+a).

The Cauchy principal value of a finite integral of a function f about a point c with a<=c<=b is given by ...