Elliptical Integrals of the First Kind Calculator

This calculator finds the elliptical integral K(k) and shows each successive step until the final result is obtained. This method of calculation is used in our Coplanar Waveguide With Ground Calculator and the equations used are shown below.

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These recursive equations were originally given for use in calculating the inductance of helical coils and are taken from Miller, H Craig, "Inductance Equation for a Single-Layer Circular Coil" Proceedings of the IEEE, Vol. 75, No 2, February 1987, pp. 256-257.

The first iteration (n₀) is calculated with the following equations.

[Equation for the first iteration of a, b, c and K(k)]

Each successive iteration is then calculated with the following equations until c_n = 0 is within the required accuracy.

[Equations for the successive iterations of a, b, c and K(k)]

When c_n = zero the value for K(k) is the required answer.

This calculator is provided free by Chemandy Electronics in order to promote the FLEXI-BOX

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Enter value k:

Iteration (n)	an	bn	cn	K(k) at iteration N = n
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K(k) = Solution