People who did that for Mathematica are world class experts (in doing calculations by hand). That's why I was surprised that Mathematica was not able to do that. Who programmed it in Maple, I don't know. Some world class expert consulting was definitely used.

Alec

People who did that for Mathematica are world class experts (in doing calculations by hand). That's why I was surprised that Mathematica was not able to do that. Who programmed it in Maple, I don't know. Some world class expert consulting was definitely used.

Alec

The situation with MeijerG is very similar to the situation with differentiation and integration.

Differentiation is a simple operation that can be done using tables of derivatives and few simple rules. The same for conversions to MeijerG - they can be done using tables and simple rules.

Integration is an inverse operation, which also can be done in some cases with tables and few rules, but some of the rules (such as integration by parts, or substitution) have the problem that it is not clear when they should be applied and when not, plus they have various choices - both in integration by parts and substitution. Exactly the same situation for conversions from MeijerG to standard functions. Plus in some cases a normal way of doing it is through integration.

So it seems as if using MeijerG for integration may be not such a great idea as it looked originally.

Alec

The situation with MeijerG is very similar to the situation with differentiation and integration.

Differentiation is a simple operation that can be done using tables of derivatives and few simple rules. The same for conversions to MeijerG - they can be done using tables and simple rules.

Integration is an inverse operation, which also can be done in some cases with tables and few rules, but some of the rules (such as integration by parts, or substitution) have the problem that it is not clear when they should be applied and when not, plus they have various choices - both in integration by parts and substitution. Exactly the same situation for conversions from MeijerG to standard functions. Plus in some cases a normal way of doing it is through integration.

So it seems as if using MeijerG for integration may be not such a great idea as it looked originally.

Alec

Mathematica 6.03 can't do that either. And numerically evaluates that value of MeijerG to a complex number with a small imaginary part.

Special functions seems to be a field where humans still beat computers - in spite of all 20-year old and 10-year old predictions.

Alec

Mathematica 6.03 can't do that either. And numerically evaluates that value of MeijerG to a complex number with a small imaginary part.

Special functions seems to be a field where humans still beat computers - in spite of all 20-year old and 10-year old predictions.

Alec

It looks like an obvious thing to do - if an integrand is a sum of 2 terms, integrate each of them and then add.

Did this problem start in Maple 12 or earlier?

Alec

It looks like an obvious thing to do - if an integrand is a sum of 2 terms, integrate each of them and then add.

Did this problem start in Maple 12 or earlier?

Alec

Maple is not able to do the original integral even in the Classic Interface.

Here is another example, more simple, that Maple has problems with,

int(1+(x^2)^(1/3),x);
                           /
                          |        2 (1/3)
                          |  1 + (x )      dx
                          |
                         /

Without adding 1, it works OK,

int((x^2)^(1/3),x);
                                   2 (1/3)
                           3/5 x (x )

Alec

Maple is not able to do the original integral even in the Classic Interface.

Here is another example, more simple, that Maple has problems with,

int(1+(x^2)^(1/3),x);
                           /
                          |        2 (1/3)
                          |  1 + (x )      dx
                          |
                         /

Without adding 1, it works OK,

int((x^2)^(1/3),x);
                                   2 (1/3)
                           3/5 x (x )

Alec

irem, probably, could be used, or convert(n,base,2). Also, you might look for other than Maple interpreter - Python, for instance (and it's free.)

Alec

irem, probably, could be used, or convert(n,base,2). Also, you might look for other than Maple interpreter - Python, for instance (and it's free.)

Alec

Last time I checked, the implementation of Heun functions was very incomplete, and none of the conversions to or from them was supported. Perhaps, it has changed by now, and they were not added to the help page list for some other reason.

Alec

Last time I checked, the implementation of Heun functions was very incomplete, and none of the conversions to or from them was supported. Perhaps, it has changed by now, and they were not added to the help page list for some other reason.

Alec

Is it flex/bison (or Flex/Bison :) or some other kind of lex/yacc? Java interface seems to be using something different.

Alec