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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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