Talk:Principal value

This article emphasizes the tight relation between principal and complex values. Could happen this is an important case, though, I feel, not necessary and therefore misleading. The confusion forced me to check the Wolfram Mathworld definition: "The principal value of an analytic multivalued function is the single value chosen by convention to be returned for a given argument". So, the basic illustration would be a function well-known to any student, e.g. arccos(1) = 0+2Πk. Meantime, the complex numbers are a high math and the ambiguities of complex multi-valued functions should be considered in a separate principal branches arthicle for advanced mathematicians, IMHO.--Javalenok 13:16, 8 January 2006 (UTC)

The term "principal value" can also refer to the value of inverse trigonometric functions in the range -pi/2 to pi/2 for arcsine and arccos, and the range 0 to pi for arctangent. Does this belong here or should another article be created with disambiguation? —Preceding unsigned comment added by DEMcAdams (talk • contribs) 12:08, 31 October 2010 (UTC)

principal value mod n
I believe the concept of Principal value is also used to refer to the value in the range 0 .. n - 1 that is equivalent to some argument (mod n). I was expecting to find a reference to that here, and hoping to find standard notation for it. If I'm right to believe that, I suggest it would be useful to add it (either here, or separately via dab). Hv (talk) 07:50, 21 June 2017 (UTC)

Obfuscation
Starting out with an example involving complex logarithms seems designed to turn readers away. As Javalenok pointed out the same example can be given with trig functions: The sine of 30* is 0.5. A solution to (x = arcsin(0.5) is thus obviously 30*. However 30* plus any integral multple of 360* (2pi) is also a solution. By convention, the principle value of arcsin(y) is taken to be in the range . . . Eaberry (talk) 05:01, 13 November 2017 (UTC)

Body
LaTeX or whatever Wikipedia uses should be used in the body text. italicised i and the unicode pi don't read well. — Preceding unsigned comment added by 208.185.122.64 (talk) 19:17, 14 January 2022 (UTC)

The(??) principal value
The article is inconsistent with itself. In some cases it indicates that the choice of branch cut and sheet are already determined (e.g., "The branch corresponding to $k = 0$ is known as the principal branch"), and in other places the article indicates that one is free to choose the branch cut and sheet to thus specify what is meant by principal value (e.g., "The principal value of [a] complex number argument measured in radians can be defined as: values in the range $[0, 2\pi)$ [or] values in the range $(−\pi, π]$").

I recommend that the article be mostly the latter; that one is free to choose what one means by principal value in any given treatise. We would nonetheless note that some choices are ubiquitous; e.g., the principal value of the square root of a positive real number is, quite generally, the positive value.

Whichever way we go, citations to back it up would be great! Do you have any? — Q uantling (talk &#124; contribs) 14:22, 28 February 2023 (UTC)