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The Maxima on-line user's manual

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Elliptic_pi

Function: elliptic_pi (<n>, <phi>, <m>) The incomplete elliptic integral of the third kind, defined as

integrate(1/(1-n*sin(x)^2)/sqrt(1 - m*sin(x)^2), x, 0, phi)

Only the derivative with respect to phi is known by Maxima.

(%o1)                                true
(%i2) 

Related Examples

pi-romberg-sin

romberg(romberg(sin(x...

Calculate

pi-plot2d-sin-sqrt
plot2d(A*%pi,[x,-5,5]);

A:sin(x);

sigma: 1;

scale: 1/sqrt(2*sigma...

Calculate

pi-plot2d-sin-sqrt-taylor
plot2d([f1(x),f(x)],[x,0,2],[y,-10,10],[color,blue,red]);

f(x):=sqrt(sin(x*%pi)...

f1(x):=taylor(f(x),x,...

plot2d([f1(x),f(x)],[...

Calculate

pi-plot2d-sin
plot2d (sin(x+2*%pi), [x, 0, %pi],[y,-2,2]);

plot2d (sin(x+2*%pi),...

Calculate

pi-plot2d-sin
plot2d ([sin(x),(2/%pi)*x], [x, -2*%pi, 2*%pi],[y, -1.1, 1.1]);

plot2d ([sin(x),(2/%p...

plot2d ([sin(x),(2/(...

plot2d ([sin(x),(2/(9...

Calculate

pi-sqrt

sqrt(16200+(12+24*t-1...

Calculate

pi-tan

\pi;

'tan((3/2)*pi+a)^2 - ...

Calculate

pi-plot2d
plot2d(I(t),[t,0,6*tau]);

pi:3.141592653589793;

U1:40;

U2:800;

Calculate

pi

((((%pi)^2/3)-4)*(sum...

Calculate

pi-plot2d
plot2d(h1(t),[t,-%pi, %pi]);

h1(t):= if mod(t,2*%p...

plot2d(h1(t),[t,-%pi,...

Calculate