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MathGroup Archive 1996

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Re: Calculating Sums Of Roots For Trans. Functions

  • To: mathgroup at smc.vnet.net
  • Subject: [mg5532] Re: [mg5498] Calculating Sums Of Roots For Trans. Functions
  • From: "w.meeussen" <w.meeussen at solair4b.eunet.be>
  • Date: Thu, 19 Dec 1996 01:02:31 -0500
  • Sender: owner-wri-mathgroup at wolfram.com

At 19:26 14-12-96 -0500, you wrote:
>Can anyone help?
>
>How do i calculate the first n roots of tan(z) = -z, and then sum them in
>one command.
>
>I think i need the right combinations of Findroot, Table and N/Sum commands.
>
>Findroot and Table give me a non-unique and non-ordered set of roots e.g.
>
> RootTable = Table[{FindRoot[Tan[z]==-z, {z,i},
>        MaxIterations ->50],i},{i,0,EndRange,Pi}]
>                // TableForm
>
>
>In short, i'd like a procedure/command that essentially sums the first n
>(unique and ordered) roots
> of tan(z) = - z with no user intervention
>
> Any ideas??
>
>thanks frank
>
>--------------------------------------------------------------------------
>Dr Frank Stagnitti
>School of Computing and Mathematics, Deakin University,
>P.O. Box 423, Warrnambool, Vic. 3280 AUSTRALIA
>Email:  frankst at deakin.edu.au
>Voice:  +61 (0)55 633 535
>WWW:    http://www.cm.deakin.edu.au/~frankst
>
>"Imagination is more important than knowledge."  (Albert Einstein)
>--------------------------------------------------------------------------
>
>
>

does this help (partially) to get you going ?

EndRange=24 
RootTable =Table[{i, FindRoot[Tan[z]==-z,{z, i Pi,(i-1/2)Pi,(i+1/2) Pi},
MaxIterations->50]},{i,1,EndRange,2}]//InputForm

EndRange=24 
RootTable =Table[{i, FindRoot[Tan[z]==-z,{z, i Pi,(i-1/2)Pi,(i+1/2) Pi},
MaxIterations->50]},{i,1,EndRange,2}]//InputForm

24

FindRoot::regex: Reached the point {4.71239} which is outside the region
{{7.85398, 10.9956}}.
FindRoot::regex: Reached the point {7.85398} which is outside the region
{{14.1372, 17.2788}}.
FindRoot::regex: Reached the point {10.9956} which is outside the region
{{20.4204, 23.5619}}.
General::stop: Further output of FindRoot::regex will be suppressed during
this calculation.

{{1, {z -> 2.028757838110434}}, {3, {z -> 4.71238898038469}}, {5, {z ->
7.853981633974483}}, 
  {7, {z -> 10.99557428756428}}, {9, {z -> 14.13716694115407}}, {11, {z ->
17.27875959474386}}, 
  {13, {z -> 20.42035224833366}}, {15, {z -> 23.56194490192345}}, {17, {z ->
26.70353755551325}}, 
  {19, {z -> 29.84513020910304}}, {21, {z -> 32.98672286269283}}, {23, {z ->
36.12831551628262}}}

Tan[z]+z/.#& /@(Flatten[Rest/@%])//InputForm

{-(8.88178419700125*10^-16), 5.443926242794622*10^15,
3.266355745676778*10^15, 2.333111246911989*10^15, 
  1.814642080931553*10^15, -(9.06763539887886*10^14),
-(1.020030638044137*10^15), -(1.165634202629249*10^15), 
  -(1.359727569653867*10^15), -(1.631372458431061*10^15),
-(2.038652160436455*10^15), 3.140058399004482*10^14}


Wouter.
Dr. Wouter L. J. MEEUSSEN
w.meeussen at solair4b.eunet.be



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