```Date: May 29, 2010 3:00 PM
Author: stargene@sbcglobal.net
Subject: Is there a compact form for n-tuple relativistic additions of <br>	velocities?

I seek advice on whether a certain very long function can be madesignificantly more compact and therefore easier to compute.I am interested in calculating the value of a function which resemblesboth a continued fraction and an iterated function, where the basicunit of the iteration is the right hand side of the formula forrelativisticaddition of two (collinear) velocities:(1)  W_1 = (u + v) / (1+uv) .u and v are the summed velocities, given as decimal fractions of thevelocity of light C.  Ie: u,v range from 0.0 to 1.0 .  Their resultantvelocity is W_n.The essential idea is to divide C into n <equal> velocities (v) andthenadd them sequentially.  My procedure is to take the first sum, W, andthen add to it a third identical velocity v, which gives a secondresultantvelocity(2)  W_2 = (W_1 + v) / (1 + vW_1) .This is an iteration of the basic form in (1).Similarly, a fourth identical velocity v is added to W_2, giving(3)  W_3 = (W_2 + v) / (1+ vW_2) ,and so on and on...This is to be repeated n times, where n becomes very large andv commensurately smaller.  I wish to know the values of this functionas n becomes extremely large.  I especially want to know what thefunction converges to as n ---> infinity and C/n ---> zero velocity.A partial glimpse of this procedure as a single large relationresemblesan unusual variety of continued fraction.  I omit rendering it in ASCIIform here since it rapidly becomes very confusing and opaque.Any feedback will be very appreciated.Thanks,Gene
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