Question

Eular's Theorem on Homogeneous Function...give me proof of this theorem

Answer 1

Calculus and Analysis > Functions >


Euler's Homogeneous Function Theorem



Let f(x:y) be a homogeneous function of order n 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.