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Given a Jacobi amplitude phi and a elliptic modulus m in an elliptic integral, Delta(phi)=sqrt(1-msin^2phi).

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

The computation of a derivative.

Any pair of equations giving the real part of a function as an integral of its imaginary part and the imaginary part as an integral of its real part. Dispersion relationships ...

The involute of an ellipse specified parametrically by x = acost (1) y = bsint (2) is given by the parametric equations x_i = ...

A parameter n used to specify an elliptic integral of the third kind Pi(n;phi,k).

A function which arises in the fractional integral of e^(at), given by E_t(nu,a) = (e^(at))/(Gamma(nu))int_0^tx^(nu-1)e^(-ax)dx (1) = (a^(-nu)e^(at)gamma(nu,at))/(Gamma(nu)), ...

If P(x,y) and P(x^',y^') are two points on an ellipse (x^2)/(a^2)+(y^2)/(b^2)=1, (1) with eccentric angles phi and phi^' such that tanphitanphi^'=b/a (2) and A=P(a,0) and ...

Let f(theta) be Lebesgue integrable and let f(r,theta)=1/(2pi)int_(-pi)^pif(t)(1-r^2)/(1-2rcos(t-theta)+r^2)dt (1) be the corresponding Poisson integral. Then almost ...

The ring of fractions of an integral domain. The field of fractions of the ring of integers Z is the rational field Q, and the field of fractions of the polynomial ring ...