Typographic Error

There is a typographic error discovered in class in equation (7.9) of Iserlies. The correct equation should read ${\cal D}^{2s} ={1\over h^{2s}} \big[(\Delta_0^2)^s-{\textstyle{1\over 12}} (\Delta_0^2)^{s+1}+{\textstyle{1\over 90}} (\Delta_0^2)^{s+2}\big] + {\cal O}(h^6), \quad h\to 0.$ This is supported by the following calculation in Maple:

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> Order:=8;
                                  Order := 8

> g:=xi->log(xi+sqrt(1+xi^2));
                                                     2
                      g := xi -> log(xi + sqrt(1 + xi ))

> R1:=series(2/h*g(d0/2),d0);
                           3              5               7      8
 R1 := 1/h d0 - 1/24 1/h d0 + 3/640 1/h d0 - 5/7168 1/h d0 + O(d0 )

#Following is line (7.8) calculated for D^2

> R2:=series(R1*R1,d0);

                   1     2         1     4         1     6       8
            R2 := ---- d0  - 1/12 ---- d0  + 1/90 ---- d0  + O(d0 )
                    2               2               2
                   h               h               h
> quit
bytes used=296344, alloc=262096, time=0.03

Last updated: Tue Jan 28 07:15:27 PST 2003