From: Walter Roberson on 19 Apr 2010 16:00 Walter Roberson wrote: > Nathan Zhang wrote: > >> Even the value of "nu" is from 0 to +infinity as integer, how to find >> the sum?? > > You cannot. The besselh documentation indicates that besselh is not > defined when nu is an integer. If you examine the definition of besselh, > you will see there is a sin(nu*Pi) in the denominator, and that is > going to be 0 for every integer nu . I have sent a service request to Mathworks on this matter. Mathworks documents the individual components of the equations as being equivalent to besselj and bessely, and if you examine either of those you will see that they imply that integral v is common for their inputs. The documentation may be incorrect in requiring non-negative non-integral v (nu). Whether the documentation is correct or not, it is the case that there is no easily calculable closed-form function for the summation you are requesting.
From: Walter Roberson on 21 Apr 2010 13:21 Walter Roberson wrote: > My symbolic package is telling me that > simplify(convert(Sum(f,n=-10..10),Int)) is 0, but with numeric > substitution, I think it is mistaken. With some assistance from other users, I have proven that the above is a bug in the symbolic package I am using, that the conversion to integral form should _not_ result in 0 for the summation. Unfortunately, the formula that I am able to come up with do not appear to have any closed form. It appears to me that as you add more and more components (extend the summation further and further towards infinity) that you will more and more closely approximate something akin to a trapazoid or possibly parallelagram wave. The exp() part you have in the numerator would, by itself, have a limit that was a square wave (I think), but the besselh in the denominator adds a slightly different phase correction to each of the sine waves. I could be misinterpreting.
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