# Dividing Lamé coefficients

LagrangeEuler
Sometimes in calculations authors uses
$$\frac{1}{h_1h_2}=\frac{h_3}{h_1h_2h_3}$$
where ##h_i, i=1,2,3## are Lame coefficients. For instance in spherical coordinates ##h_r=1##, ##h_{\theta}=r##, ##h_{\varphi}=r\sin \theta##. I am not sure how we can divide so easily Lame coefficients when some on them obviously can be zero for certain values of parameters. Can someone give me some explanation? Thanks a lot in advance.

## Answers and Replies

Gold Member
I have no background of the physics there but the formula seems multiplying the same number to denominator and numerator, so obviously right except the number is zero.

Mentor
Changed problem level from A to B. The underlying concept of Lame coefficients might be advanced, but in the posted problem all that was done was to multiply a fraction by 1 in the form of ##h_3## over itself.

Homework Helper
2022 Award
I am not sure how we can divide so easily Lame coefficients when some on them obviously can be zero for certain values of parameters. Can someone give me some explanation? Thanks a lot in advance.

You can divide a function by another function provided that the denominator is not identically zero; this reduces the domain by excluding points where the denominator is zero. In the context of Lame coefficients these are points where the coordinate system breaks down, with a single point being referred to by multiple distinct coordinate tuples. If you need to analyze something at these points, the answer is to use a different coordinate system.