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The Maxima on-line user's manual

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Elliptic_kc

Function: elliptic_kc (<m>) The complete elliptic integral of the first kind, defined as

load(romberg);
romberg((3-cos(x))^(-1/2),x,0,%pi/2);
float(elliptic_kc(1/sqrt(2))-elliptic_f(%pi/4,1/sqrt(2)))-%;
plot2d((3-cos(x))^(-1/2),[x,0,%pi/2]);

integrate(1/sqrt(1 - m*sin(x)^2), x, 0, %pi/2)

For certain values of m, the value of the integral is known in terms of Gamma functions. Use makegamma to evaluate them.

(%o1)                                true
(%i2) 

Related Examples

elliptic_kc

elliptic_kc (5./9);

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elliptic_kc (1/3);

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elliptic_kc

elliptic_kc (1/3) ;

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elliptic_kc

elliptic_kc (1/4) ;

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elliptic_kc

elliptic_kc (1/3) ;

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elliptic_kc

elliptic_kc (m);

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elliptic_kc-plot2d
plot2d([elliptic_kc(k)],[k,0,0.5]);

plot2d([elliptic_kc(k...

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elliptic_kc

elliptic_kc (5./9);

Calculate

elliptic_kc

elliptic_kc (1/3) ;

Calculate

elliptic_kc-plot2d
plot2d([elliptic_kc(k)],[k,0,1]);

plot2d([elliptic_kc(k...

Calculate