10/29/2009, 01:55 PM

(10/29/2009, 12:08 PM)bo198214 Wrote: Why is this not published as a proper book?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.

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.

Here is a msg of si.math, which I saved when I came across it:

see also google groups

Code:

`Betreff: Online "book" about solution of y=x^x`

Von:"L" <believe@ptw.com>

Datum:Thu, 20 Jul 2000 17:47:57 -0700

Hello SCI.MATH,

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:

http://www.networkone.net/~believe

Questions and comments can be sent to believe@networkone.net 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

y=wzl(x).

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:

A

y = ------

B

WZL(-)

x

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.

-Jay

Code:

`Betreff:Re: Wexzal book`

Von:"lori" <lori1@antelecom.net>

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

arguments.

See TETRATION in google for more info.

[...]

-Jay

Gottfried Helms, Kassel