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A repeated integral is an integral taken multiple times over a single variable (as distinguished from a multiple integral, which consists of a number of integrals taken with ...

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 ...

If g is continuous and mu,nu>0, then int_0^t(t-xi)^(mu-1)dxiint_0^xi(xi-x)^(nu-1)g(xi,x)dx =int_0^tdxint_x^t(t-xi)^(mu-1)(xi-x)^(nu-1)g(xi,x)dxi.

An integral which has neither limit infinite and from which the integrand does not approach infinity at any point in the range of integration.

Integral calculus is that portion of "the" calculus dealing with integrals. Among his many other talents, Major General Stanley in Gilbert and Sullivan's operetta The Pirates ...

alpha_n(z) = int_1^inftyt^ne^(-zt)dt (1) = n!z^(-(n+1))e^(-z)sum_(k=0)^(n)(z^k)/(k!). (2) It is equivalent to alpha_n(z)=E_(-n)(z), (3) where E_n(z) is the En-function.

Since the derivative of a constant is zero, any constant may be added to an indefinite integral (i.e., antiderivative) and will still correspond to the same integral. Another ...

Integrals of the form intf(costheta,sintheta)dtheta (1) can be solved by making the substitution z=e^(itheta) so that dz=ie^(itheta)dtheta and expressing costheta = ...

The (complete) gamma function Gamma(n) is defined to be an extension of the factorial to complex and real number arguments. It is related to the factorial by Gamma(n)=(n-1)!, ...

A second-order algebraic surface given by the general equation (1) Quadratic surfaces are also called quadrics, and there are 17 standard-form types. A quadratic surface ...