First three terms of the TM series for x

For , , , ,

E is the truncation error, and where is a small parameter of the ERM,

the series expansion for X is given by,

This is an alternating series which depends on latitude, longitude,

longitude of the origin, and the eccentricity of the ERM.

Note that E is small only if delta is small

and the latitude does not get too near 90º.

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