use the substitution v = sinx to rewrite the elliptic integrals in terms of v and z = siny
E(k,y) = [integral from 0 to y] SQRT( 1 - (ksinx)^2) dx
F(k,y) = [integral from 0 to y] dx / (SQRT(1 - (ksinx)^2)
II(k,y) = [integral from 0 to y] dx / ((1 + n(sinx)^2)SQRT(1 - (ksinx)^2))
i keep getting stuck... for example the substitution v= sinx for the elliptic integral F:
subst. v = sinx
i.e. x = arcsin v
dx = 1/SQRT(1-v^2) * dv
= [integral from 0 to siny] dv / (SQRT( 1-v^2) * SQRT(1 -(ksinx)^2)) ... what do I do from here?
E(k,y) = [integral from 0 to y] SQRT( 1 - (ksinx)^2) dx
F(k,y) = [integral from 0 to y] dx / (SQRT(1 - (ksinx)^2)
II(k,y) = [integral from 0 to y] dx / ((1 + n(sinx)^2)SQRT(1 - (ksinx)^2))
i keep getting stuck... for example the substitution v= sinx for the elliptic integral F:
subst. v = sinx
i.e. x = arcsin v
dx = 1/SQRT(1-v^2) * dv
= [integral from 0 to siny] dv / (SQRT( 1-v^2) * SQRT(1 -(ksinx)^2)) ... what do I do from here?