J F Ogilvie

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19 years, 185 days

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These are questions asked by J F Ogilvie

Some years ago it was promised that expansion of capabilities of Heun functions was imminent, but nothing has appeared.  Other functions long overdue for inclusion as special functions in Maple are the Lame functions, which arise as special cases of Heun's differential equation and therefore of Heun functions.  Lame's differential equation appears in Abramowitz and Stegun, but has long been neglected in Maple.  These spectial functions are much more generally useful to users of Maple than, for instance, esoteric parts of the physics package. 

The integral of y = Dirac(phi-m), in which phi is a continuously variable quantity and m is a positive integer, from -infinity to infinity yields 1 as an answer.   The analogous integral of y2 yields no answer.  Is it possible that the latter integral has some mathematical meaning that might yield an answer?

A research paper published in 1929 claimed that this integral was solved in 1896.

int(exp(I*m*omega + I*b*cos(omega) ),omega=0..2*Pi)           (m integer,  b positive constant)

but it defeats Maple (and other).  Can anybody suggest a way to solve this integral with Maple?


To ensure the general accessibility of my Maple worksheets for Mathematics for Chemistry, I work with the classic interface.  When I tried to install first Maple 2018.1, when it became available, and then Maple 2018.2 when it became available, the output from use of either technical input in text lines, using function key F5, or simply from an executable input command or statement was corrupted.  I reported this behaviour but apparently the remedy has not yet been incorporated.  To avoid these problems, I had to delete Maple 2018.2 and to reinstall Maple 2018.0.  

     When I, in good faith, with that Maple 2018.0 reinstalled tried to install Maplesoft Physics Updates version 241, according to the encouragement of Edgardo Cheb-Terrab above, I discovered the same corruption in the output when I entered a procedure, for instance this one,

ft := proc(kk,ll,mm)
>      h^(-3/2)*int(int(int(expand(exp(-(2*Pi*I/h)*(sin(theta)*sin(Theta)*cos(Phi-phi)+cos(theta)*cos(Theta))*r*P)
>            *eval(psi,[k=kk,l=ll,m=mm])*r^2*sin(theta), trig),phi=0..2*Pi),theta=0..Pi),r=0..infinity);
> end proc;
  ft := proc(kk, ll, mm)
    1/h^(3/2)*int(int(int(expand(exp(-2*I*Pi*(in(theta)*sin(Theta)*cos(Phi - phi)+ cos(theta)*cos(Theta))*r*P/h)*eval(psi, [k = kk, l = ll,  m = mm])*r^2*sin(theta), trig), phi = 0 .. 2*Pi), theta = 0 .. Pi), r = 0 .. infinity)
end proc

namely that, instead of * in any location in the output that you can read above, there appears a large U.  Why is the testing by Dr. Cheb-Terrab and others connected with Maplesoft done in such a slipshod manner?  After all these years one should expect better control of quality than is evidently the case.  It seems that I must once again reinstall Maple 2018.0 to regain the full functionality of Maple 2018 without the deficiencies introduced in both the updates and the Physics package.  This condition is disgraceful and intolerable.

A few days ago I was browsing through some books in my collection, that by Gradshteyn and Ryzhik in particular. What fraction of the intregrals, series and products therein can Maple handle correctly?  Besides special functions these properties are valuable components of symbolic mathematical software.  If the answer to this question is not nearly everything in that printed compilation, this inclusion in Maple is a worthy objective.

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