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Re: [Help-gsl] computing nth root of beta tan(beta) = L

From: Agile Aspect
Subject: Re: [Help-gsl] computing nth root of beta tan(beta) = L
Date: Tue, 13 May 2008 20:42:57 -0700
User-agent: Thunderbird (X11/20080421)

Levi Waldron wrote:
Is there a GSL function for computing the nth positive root of
beta*tan(beta) = L for arbitrary values of L?  I couldn't find it in the
manual, but not all special functions give their specifications in the
manual and I don't know what this equation is called.  It is used in the
plane sheet solution of the heat/diffusion equation with type II (Neumann)
boundary condition.

You could plot tan(beta) and L/beta as a function of beta on the
same graph and find their intersections

Since tan has multiple branches,  then it might be possible to find
an approximate closed expression for beta for large values of n.

Or, alternatively, for small values of beta, approximate tan(beta) as
a truncated power series and solve the polynomial.

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