(28/48/50) Lambert W Function

[Gil]

Hi, Albert.

With your function definition of post 20,

1) could I modify as follows?

200 DEF FNL(X) !
« —> X
«210 IF ABS(X)>=.4
THEN X=X/(SQRT(1+X)+1) @ L=FNL(X)*2-X*X
ELSE
220 X2=X/(X+2) @ X4=X2*X2
230 X4=X4*(5005-X4*(5082-X4*969))/(15015-X4*(24255-X4*(11025-X4*1225)))
240 L=X2*(X4+X4-X)
250 END
»
»

for my HP50G calculator program.

2) Could I, consequently, simplify "your" line 42 as follows?

42 DO FNL(X) @Z=X-(H-L)/(X+L) @ X=X-Z @ UNTIL X=X+Z*.0001 END
44 PRINT "e^W, W =";R+R*X;LOGP1(X)-1

3) And I should start the program with line 40 defined as before
>40 H=(A+R+R2)/R @ X=SQRT(2*H)*K @ X=X*SQRT(1+X/3) @ Y=R+R*X

Correct?

In fact, it seems that L cannot be equal to @ L=FNL(X)*2-X*X

Or the defined function should be rather
200 DEF FNL(X) !
« —> X
«210 IF ABS(X)>=.4
THEN X=X/(SQRT(1+X)+1) @ L=X*2-X*X
ELSE
220 X2=X/(X+2) @ X4=X2*X2
230 X4=X4*(5005-X4*(5082-X4*969))/(15015-X4*(24255-X4*(11025-X4*1225)))
240 L=X2*(X4+X4-X)
250 END

Thanks again, Albert, for your possible and always precious help.

Gil