## Re: [Maxima-discuss] Nesting an integral inside a limit

 Re: [Maxima-discuss] Nesting an integral inside a limit From: James Hozier - 2014-06-04 16:32:40 Attachments: Message as HTML ```Psi is the balanced polygamma function, which I believe in Maxima is bfpsi. How can I format it so that Maxima can recognize the integral inside the limit? On Wed, Jun 4, 2014 at 12:09 PM, Raymond Toy wrote: > >>>>> "James" == James Hozier writes: > > James> I am trying to do: limit(1 / n^2 * integrate(bfpsi(-2,x+1,16) * > (sin((2n - 1)*x) / sin(x))^3, x, 0, > James> %pi / 2), n, inf); > > > James> But I get a bunch of syntax errors, presumably because I'm > trying to put an integral inside a > James> limit. For ease of visibility, here in LaTeX typeset is what > the problem should appear as: > James> http://i.imgur.com/vjzIp5f.gif > > Several things are wrong here. 2n should be written 2*n. And based on > the image, I think bfpsi(-2,x+1,16) is not what you want. I think the > image says 1/psi(x+1)^2. > > In any case, I suspect maxima can't do the limit because maxima can't > figure out what the integral looks like. > > Ray > > > > ------------------------------------------------------------------------------ > Learn Graph Databases - Download FREE O'Reilly Book > "Graph Databases" is the definitive new guide to graph databases and their > applications. Written by three acclaimed leaders in the field, > this first edition is now available. Download your free book today! > http://p.sf.net/sfu/NeoTech > _______________________________________________ > Maxima-discuss mailing list > Maxima-discuss@... > https://lists.sourceforge.net/lists/listinfo/maxima-discuss > ```

 [Maxima-discuss] Nesting an integral inside a limit From: James Hozier - 2014-06-04 14:41:51 Attachments: Message as HTML ```I am trying to do: limit(1 / n^2 * integrate(bfpsi(-2,x+1,16) * (sin((2n - 1)*x) / sin(x))^3, x, 0, %pi / 2), n, inf); But I get a bunch of syntax errors, presumably because I'm trying to put an integral inside a limit. For ease of visibility, here in LaTeX typeset is what the problem should appear as: http://i.imgur.com/vjzIp5f.gif How can I input this type of problem into wxMaxima? ```
 Re: [Maxima-discuss] Nesting an integral inside a limit From: Raymond Toy - 2014-06-04 16:09:43 ```>>>>> "James" == James Hozier writes: James> I am trying to do: limit(1 / n^2 * integrate(bfpsi(-2,x+1,16) * (sin((2n - 1)*x) / sin(x))^3, x, 0, James> %pi / 2), n, inf); James> But I get a bunch of syntax errors, presumably because I'm trying to put an integral inside a James> limit. For ease of visibility, here in LaTeX typeset is what the problem should appear as: James> http://i.imgur.com/vjzIp5f.gif Several things are wrong here. 2n should be written 2*n. And based on the image, I think bfpsi(-2,x+1,16) is not what you want. I think the image says 1/psi(x+1)^2. In any case, I suspect maxima can't do the limit because maxima can't figure out what the integral looks like. Ray ```
 Re: [Maxima-discuss] Nesting an integral inside a limit From: James Hozier - 2014-06-04 16:32:40 Attachments: Message as HTML ```Psi is the balanced polygamma function, which I believe in Maxima is bfpsi. How can I format it so that Maxima can recognize the integral inside the limit? On Wed, Jun 4, 2014 at 12:09 PM, Raymond Toy wrote: > >>>>> "James" == James Hozier writes: > > James> I am trying to do: limit(1 / n^2 * integrate(bfpsi(-2,x+1,16) * > (sin((2n - 1)*x) / sin(x))^3, x, 0, > James> %pi / 2), n, inf); > > > James> But I get a bunch of syntax errors, presumably because I'm > trying to put an integral inside a > James> limit. For ease of visibility, here in LaTeX typeset is what > the problem should appear as: > James> http://i.imgur.com/vjzIp5f.gif > > Several things are wrong here. 2n should be written 2*n. And based on > the image, I think bfpsi(-2,x+1,16) is not what you want. I think the > image says 1/psi(x+1)^2. > > In any case, I suspect maxima can't do the limit because maxima can't > figure out what the integral looks like. > > Ray > > > > ------------------------------------------------------------------------------ > Learn Graph Databases - Download FREE O'Reilly Book > "Graph Databases" is the definitive new guide to graph databases and their > applications. Written by three acclaimed leaders in the field, > this first edition is now available. Download your free book today! > http://p.sf.net/sfu/NeoTech > _______________________________________________ > Maxima-discuss mailing list > Maxima-discuss@... > https://lists.sourceforge.net/lists/listinfo/maxima-discuss > ```
 Re: [Maxima-discuss] Nesting an integral inside a limit From: James Hozier - 2014-06-04 16:37:04 Attachments: Message as HTML ```Actually, I'm not sure if Maxima has a different function for the negapolygamma (of order -2 in my case), so I just assumed I could use the balanced polygamma function bfpsi in Maxima. On Wed, Jun 4, 2014 at 12:09 PM, Raymond Toy wrote: > >>>>> "James" == James Hozier writes: > > James> I am trying to do: limit(1 / n^2 * integrate(bfpsi(-2,x+1,16) * > (sin((2n - 1)*x) / sin(x))^3, x, 0, > James> %pi / 2), n, inf); > > > James> But I get a bunch of syntax errors, presumably because I'm > trying to put an integral inside a > James> limit. For ease of visibility, here in LaTeX typeset is what > the problem should appear as: > James> http://i.imgur.com/vjzIp5f.gif > > Several things are wrong here. 2n should be written 2*n. And based on > the image, I think bfpsi(-2,x+1,16) is not what you want. I think the > image says 1/psi(x+1)^2. > > In any case, I suspect maxima can't do the limit because maxima can't > figure out what the integral looks like. > > Ray > > > > ------------------------------------------------------------------------------ > Learn Graph Databases - Download FREE O'Reilly Book > "Graph Databases" is the definitive new guide to graph databases and their > applications. Written by three acclaimed leaders in the field, > this first edition is now available. Download your free book today! > http://p.sf.net/sfu/NeoTech > _______________________________________________ > Maxima-discuss mailing list > Maxima-discuss@... > https://lists.sourceforge.net/lists/listinfo/maxima-discuss > ```
 Re: [Maxima-discuss] Nesting an integral inside a limit From: Raymond Toy - 2014-06-04 16:55:17 ```>>>>> "James" == James Hozier writes: James> Actually, I'm not sure if Maxima has a different function James> for the negapolygamma (of order -2 in my case), so I just James> assumed I could use the balanced polygamma function bfpsi James> in Maxima. First, bfpsi is meant for numerically evaluating the psi function for bigfloat values. You probably should use psi instead. However, psi is just the polygamma function. Ray James> On Wed, Jun 4, 2014 at 12:09 PM, Raymond Toy wrote: >>>>>> "James" == James> James Hozier writes: James>     James> I am trying to do: limit(1 / n^2 * James> integrate(bfpsi(-2,x+1,16) * (sin((2n - 1)*x) James> / sin(x))^3, x, 0, James>     James> %pi / 2), n, inf); James>     James> But I get a bunch of syntax James> errors, presumably because I'm trying to put James> an integral inside a James>     James> limit. For ease of visibility, James> here in LaTeX typeset is what the problem James> should appear as: James>     James> http://i.imgur.com/vjzIp5f.gif James> Several things are wrong here. 2n should be James> written 2*n. And based on James> the image, I think bfpsi(-2,x+1,16) is not James> what you want. I think the James> image says 1/psi(x+1)^2. James> In any case, I suspect maxima can't do the James> limit because maxima can't James> figure out what the integral looks like. James> Ray James> ------------------------------------------------------------------------------ James> Learn Graph Databases - Download FREE James> O'Reilly Book James> "Graph Databases" is the definitive new guide James> to graph databases and their James> applications. Written by three acclaimed James> leaders in the field, James> this first edition is now available. Download James> your free book today! James> http://p.sf.net/sfu/NeoTech James> _______________________________________________ James> Maxima-discuss mailing list James> Maxima-discuss@... James> https://lists.sourceforge.net/lists/listinfo/maxima-discuss James> ------------------------------------------------------------------------------ James> Learn Graph Databases - Download FREE O'Reilly Book James> "Graph Databases" is the definitive new guide to graph databases and their James> applications. Written by three acclaimed leaders in the field, James> this first edition is now available. Download your free book today! James> http://p.sf.net/sfu/NeoTech_______________________________________________ James> Maxima-discuss mailing list James> Maxima-discuss@... James> https://lists.sourceforge.net/lists/listinfo/maxima-discuss ```
 Re: [Maxima-discuss] Nesting an integral inside a limit From: Stavros Macrakis (Σταῦρος Μακράκης) - 2014-06-04 18:26:01 Attachments: Message as HTML ```Not sure what you mean by a "bunch of syntax errors". I get just one syntax error, which describes exactly what the problem is (N is not an infix operator) and points to the place in the input where the error occurred. I don't know why you'd expect a syntax error from nesting an integral inside a limit. I only wish more of our error messages were so precise! (%i1) limit(1 / n^2 * integrate(bfpsi(-2,x+1,16) * (sin((2n - 1)*x) / sin(x))^3, x, 0, %pi / 2), n, inf); incorrect syntax: N is not an infix operator ,x+1,16) * (sin((2n ^ On Wed, Jun 4, 2014 at 10:41 AM, James Hozier wrote: > I am trying to do: limit(1 / n^2 * integrate(bfpsi(-2,x+1,16) * (sin((2n - > 1)*x) / sin(x))^3, x, 0, %pi / 2), n, inf); > > But I get a bunch of syntax errors, presumably because I'm trying to put > an integral inside a limit. For ease of visibility, here in LaTeX typeset > is what the problem should appear as: http://i.imgur.com/vjzIp5f.gif > > How can I input this type of problem into wxMaxima? > > > ------------------------------------------------------------------------------ > Learn Graph Databases - Download FREE O'Reilly Book > "Graph Databases" is the definitive new guide to graph databases and their > applications. Written by three acclaimed leaders in the field, > this first edition is now available. Download your free book today! > http://p.sf.net/sfu/NeoTech > _______________________________________________ > Maxima-discuss mailing list > Maxima-discuss@... > https://lists.sourceforge.net/lists/listinfo/maxima-discuss > > ```