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Superroots (formal powerseries)
(10/29/2009, 12:08 PM)bo198214 Wrote: Why is this not published as a proper book?
I think there should be included some more data,
like finishing date and some jacket text about the authors.

And great: it contains appliations, as this really often asked and some ignorant physicists just think that there can not be applications.
Well I know nearly nothing around that text; if I google today for the authors I only find a reference at Rob. Munafo's site without presenting further reference - that's all.
Here is a msg of si.math, which I saved when I came across it:
see also google groups

Betreff: Online "book" about solution of y=x^x
Von:"L" <>
Datum:Thu, 20 Jul 2000 17:47:57 -0700


I have some items on my web site that might be of interest to those
researching equations in the form of y=x^x and related functions. This is
a topic that appears from time to time in SCI.MATH. Myself and a friend
began researching the solution of y=x^x back in 1975 while we were still
in high school. The ASCII-based "book" on my web site is a compilation
of our results from 1975 to 1995. It is written in a very informal style
that we hope is informative to users of this news group. We have included
two FORTRAN-77 files, SKRFIT.F and WEXZAL.F which are included with the
book as they implement many of the topics in the book. The web site is:

Questions and comments can be sent to and we will
try to answer questions as time permits.

The outline of the book is:

Chapter 01 - Basic discussion of y=x^x.
Chapter 02 - Inverse of x^x. This is called the Coupled Root [crt(x)].
Chapter 03 - Coupled Root of large numbers. The "Wexzal" = crt(10^x).
Chapter 04 - Closed form solution of equations via Wexzals.
Chapter 05 - Integrals involving Wexzals.
Chapter 06 - Asymptotics and limits with Wexzals.
Chapter 07 - Numerical computation of wzl(x). Calculator fans... take note!
Chapter 08 - Misc items involving Wexzals. Incomplete.
Chapter 09 - Curve-fitting with Wexzals. Incomplete.
Chapter 10 - New type of graphs involving 1/wzl(1/x).
Chapter 11 - Math model of projectile deacceleration via Wexzals.
Chapter 12 - Barrel length vs. velocity question answered with Wexzals.
Chapter 13 - Car acceleration model via Wexzals.
Chapter 14 - Equalities and inequalities of Coupled Roots & other functions.
Chapter 15 - Closed form solution of equations via Coupled Roots.
Chapter 16 - Table of integrals involving Wexzals & Coupled Roots.
Chapter 17 - Table of Asymptotic expansions and limits.
Chapter 18 - Special values and table of functions from Chapters 11-13.

The file WEXZAL.F is a collection of "home-brewed" functions and routines
that are discussed in the book. Included is the computation of the
solution of y=x^x and y=x^(x^x) along with the first 4 derivatives of

The program SKRFIT is a non-linear 2 parameter curve fitting program that
was written to solve the program of barrel lengths vs. muzzle velocity of
firearms (See chapter 12). It uses routines from WEXZAL.F which contains
the computation of WZL(x) and other items as discussed in the book.

To use the program SKRFIT after it has been compiled, one creates a
datafile that contains free-formatted (x,y) data. This data is to be fitted
in the form of:

        y = ------

where A and B are to be determined. An initial value of B is entered. This
is called B0 by the program. The value of B0 should be higher than the
expected value of B otherwise the program might not converge. An example
data set and a run of the program follows.

[...<snipped>, G.H.]

Anyway, we hope you find the "book" informative and entertaining.

I assume to have the permission to document the grant for distribution:
Betreff:Re: Wexzal book
Von:"lori" <>
Datum:Sun, 24 Nov 2002 09:15:37 -0800
Thank you for your quick reply. I just wanted to say again that
you have my permission to quote and use the Wexzal book in
anyway you see fit (just please quote the source). I am pleased
that you find it useful.

For your interest, I am currently researching tetration for real number
See TETRATION in google for more info.
Gottfried Helms, Kassel

Messages In This Thread
Superroots (formal powerseries) - by Gottfried - 10/25/2009, 12:09 PM
RE: Superroots (formal powerseries) - by andydude - 10/26/2009, 01:50 AM
RE: Superroots (formal powerseries) - by robo37 - 10/28/2009, 09:20 AM
Superroots article "WexZal" - by Gottfried - 10/29/2009, 05:56 AM
RE: Superroots article "WexZal" - by bo198214 - 10/29/2009, 12:08 PM
RE: Superroots article "WexZal" - by Gottfried - 10/29/2009, 01:55 PM
RE: Superroots article "WexZal" - by bo198214 - 10/29/2009, 10:10 PM
RE: Superroots (formal powerseries) - by Stan - 04/05/2011, 03:22 AM

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