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MathGroup Archive 1996

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Re: Re: Calculating Sums Of Roots For Trans. Functions

  • To: mathgroup at smc.vnet.net
  • Subject: [mg5583] Re: [mg5536] Re: [mg5498] Calculating Sums Of Roots For Trans. Functions
  • From: fransm at win.tue.nl (Frans Martens)
  • Date: Fri, 27 Dec 1996 01:58:58 -0500
  • Sender: owner-wri-mathgroup at wolfram.com

Allan Hayes gave an answer on the question "How do i calculate the  
first n roots of tan(z) = -z, and then sum them in one command?"
of Frank Stagnitti.

The answer was the program

Sum[ z/.FindRoot[Tan[z] == -z, {z,Pi/2 + n Pi + .02/(n+1)},
		MaxIterations ->50
	],
    {n,0,49}
 ]


Since tan(z) + z is not defined for pi/2 + n*Pi and the derivative of  
tan(z) + z  will become very large in z equal to the zero close to  
pi/2 + n*pi for greater values of n, it is better to rewrite the  
equation tan(z) = - z. 

Two suggestions:

Sum[ z/.FindRoot[Sin[z] == -z*Cos[z], {z,Pi/2 + n Pi}
	],
    {n,0,49}
 ]

Sum[ z/.FindRoot[z + n*Pi == ArcTan[-z], {z,Pi/2 + n Pi + .02/(n+1)},
		MaxIterations ->50
	],
    {n,1,50}
 ]

Frans Martens
Eindhoven
The Netherlands




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