Let 
be a homogeneous function of order 
so that
 | (1) |
Then define 
and 
. Then
 |  |  | (2) |
 |  |  | (3) |
 |  |  | (4) |
Let 
, then
 | (5) |
This can be generalized to an arbitrary number of variables
 | (6) |
where Einstein summation has been used.
Mathematics for Marine Engineering / August 6, 2021
Euler’s Homogeneous Function Theorem
Let be a homogeneous function of order so that (1) Then define and . Then (2) (3) (4) Let , then (5) This can be generalized to an arbitrary number of variables (6) where Einstein summation has been used.
