Inconsistent formulas for meridian distances
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- C++
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Description
It would be nice if `quarter_meridian`, `meridian_direct`, and `meridian_inverse` all used consistent approximations. Instead:
* `quarter_meridian` is accurate to `n^16` with the coefficient given to full precision.
* `meridian_direct` is accurate to `n^4` with the coefficients given approximately, e.g., `1.572916667` instead of `CT(151)/CT(96)`.
* `meridian_inverse` is supposed to be accurate to `n^5`, however the `n^4` contribution to `C0` and the `n^5` contribution to `C2` are omitted and the coefficients are given approximately, e.g. `-0.729166667` instead of `CT(-35)/CT(48)`.
I recommend that both `median_inverse` and `meridian_direct` include terms up to `n^6` which is needed to full double precision accuracy for the earth. If these routines used Horner and Clenshaw summation then there would be little cost in making `n^6` the minimum order provided.
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