SandorSzabo

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16 years, 200 days

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These are replies submitted by SandorSzabo

It is in the maple-12-wish-list,

http://www.mapleprimes.com/blog/jacquesc/maple-12-wish-list#comment-8640

Sandor

It is very nice!

Here S_n=sum(2^k/k, k=1..n).

I tried to calculate the Taylor series of   log(1-2*x)  / (x-1)   using

convert( log(1-2*x)  / (x-1) , FormalPowerSeries)

but Maple's answer is     log(1-2*x)  / (x-1) .

However S_n  involves LerchPhi a 2F1 hypergeometric function, so I think, in principle, the FormalPowerSeries method should give the desired answer.

Sandor

It is very nice!

Here S_n=sum(2^k/k, k=1..n).

I tried to calculate the Taylor series of   log(1-2*x)  / (x-1)   using

convert( log(1-2*x)  / (x-1) , FormalPowerSeries)

but Maple's answer is     log(1-2*x)  / (x-1) .

However S_n  involves LerchPhi a 2F1 hypergeometric function, so I think, in principle, the FormalPowerSeries method should give the desired answer.

Sandor

It is usual to approximate a sum by integral, but what can you say about the error?

It is usual to approximate a sum by integral, but what can you say about the error?

There are many books on numerical methods, I don't know this one. Could you give (approximately or exactly) the title of this book?

Thanks,   Sandor

It's a good idea. I think it would be similar to arxiv.org in principle. Instead of refereeing a community verified and updated method probably would be a good choice, similarly to some type of wikipedia. Very recently I read about a plan about a wikipedia where community can edit but there is an editorial board (above 500 leaves?, and/or phd degree?)  which makes controll on the content.

Concerning the math typing problems, I use a firefox add-on, textheworld, http://thewe.net/tex/  which instantly transforms latex to image. It works on internet based emails also, so for example I can send formulas easily in my gmail letters.

Sandor

Thanks. The improper integral is (by Maple)  arctan(2).

It's interesting that Maple does not try to determine the inverse using convolution theorem.

Or, would be an  option=conv , helping to find the inverse.

Sandor

Thanks. The improper integral is (by Maple)  arctan(2).

It's interesting that Maple does not try to determine the inverse using convolution theorem.

Or, would be an  option=conv , helping to find the inverse.

Sandor

Could you post your hand-solution? It's only my personal mathematical interest.

Thanks,   Sandor

Could you post your hand-solution? It's only my personal mathematical interest.

Thanks,   Sandor

It's a problem, but you can obtain something maybe useful.

 

Since the final result is real, you can use this fact, but probably the final result is not an elementary function.

Sandor

It's a problem, but you can obtain something maybe useful.

 

Since the final result is real, you can use this fact, but probably the final result is not an elementary function.

Sandor

Theory says: when the right hand side is a piecewise function then it is worth to try using the Laplace integral transformation.

Fortunately the dsolve has a  method=laplace  option.

Good luck!

                         Sandor

Theory says: when the right hand side is a piecewise function then it is worth to try using the Laplace integral transformation.

Fortunately the dsolve has a  method=laplace  option.

Good luck!

                         Sandor

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