I am trying to use the EllipticE and EllipticF functions in an expression. The proper function call is EllipticE(z, k) where z = algebraic expression (the sine of the amplitude) k = algebraic expression (the parameter) I get exact agreement for 0 <>< value="" value=""><><>

I have been trying to replicate the results of an analysis which uses elliptic integrals of the first and second kind (see an earlier post titled "Solve This! - Elliptic Integrals" for a copy of the analysis and a Maple worksheet that plots an equation containing an ellipitc integral). Dr. Israel provided the Maple commands that generate the plot; however, the results are not in agreement with the paper - not even close! In an attempt to validate the EllipticF(z,k) command in Maple, I have generated a spreadsheet (attached) which uses an EllipticAddin to generate a table of values for a range of phi from 1 to 45 degrees and theta over the same range. As you can see from the workbook, the Addin has successfully generated a table that is in perfect agreement to five decimal places with the results given on page 94 of "Elliptic Integrals", 1st Edition, by Harris Hancock, Wiley & Sons, 1917 (available in PDF format from Google). The sheet that uses the EllipticF(z,k) command is not in good agreement with the table from Hancock's publication.