Hi dickdock

As far as using

to denote the general value and

for the principal value: I didn't invent it, I got it from my university textbooks. So I guess people just use different conventions in different parts of the world? Not sure.

Any way (using my original convention), since

then

putting

gives

So generally

Also if

then multiplying both sides by

gives

In our cases below and elsewhere, this

can always be absorbed into

as shown above.

Quote:

If we can just equate exponentials, is there anything to prove (as you seem to say in the note at the end), since

Q.E.D. (As it 'appens that's what I wrote in my copy of the book originally, before I made the tragic mistake of visiting this forum.)

This is not correct. We are trying to show that if we choose

a certain value for

in (3), out of the infinity of values it can have, and we call that value

,

then we must choose, out of the infinity of values that in (2) can have, the value

.

You must always remember that (2) and (3) in my original post are

multivalued and from looking at (3) and (5) it is clear that they are equal only under certain conditions.

If (2) and (3)

are to be equal and

for (3) is chosen as

, then