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The third singular value k_3, corresponding to K^'(k_3)=sqrt(3)K(k_3), (1) is given by k_3=sin(pi/(12))=1/4(sqrt(6)-sqrt(2)). (2) As shown by Legendre, ...

For |z|<1, product_(k=1)^infty(1+z^k)=product_(k=1)^infty(1-z^(2k-1))^(-1). (1) Both of these have closed form representation 1/2(-1;z)_infty, (2) where (a;q)_infty is a ...

The Fibonacci factorial constant is the constant appearing in the asymptotic growth of the fibonorials (aka. Fibonacci factorials) n!_F. It is given by the infinite product ...

The modular group Gamma is the set of all transformations w of the form w(t)=(at+b)/(ct+d), where a, b, c, and d are integers and ad-bc=1. A Gamma-modular function is then ...

tau is the ratio tau=omega_2/omega_1 of the two half-periods omega_1 and omega_2 of an elliptic function (Whittaker and Watson 1990, pp. 463 and 473) defined such that the ...

An integral of the form intf(z)dz, (1) i.e., without upper and lower limits, also called an antiderivative. The first fundamental theorem of calculus allows definite ...

An indicial equation, also called a characteristic equation, is a recurrence equation obtained during application of the Frobenius method of solving a second-order ordinary ...

The König-Egeváry theorem, sometimes simply called König's theorem, asserts that the matching number (i.e., size of a maximum independent edge set) is equal to the vertex ...

The ordinary differential equation (1) (Byerly 1959, p. 255). The solution is denoted E_m^p(x) and is known as an ellipsoidal harmonic of the first kind, or Lamé function. ...

The quintuple product identity, also called the Watson quintuple product identity, states (1) It can also be written (2) or (3) The quintuple product identity can be written ...