Odd/even for a multivariable function

[wumple]

Is the definition of an odd/even function in multiple variables what I would expect it to be, ie

$$f(-x,-y)=-f(x,y)$$

Thanks!

 

[mathwonk]

yes that is the standard definition. Sometimes I have a family of odd or even functions however, i.e. the functions involve two kinds of variables, the variables of the functions, and the variables that parametrize the family. Then they are only odd or even in the first set of variables.e.g. a family of even functions of x,y, parametrized by z, might be represented as a single function F(x,y;z) such that for all x,y,z we have F(-x,-y;z) = F(x,y;z).i.e. for each value of z, say z=c, the function F(x,y;c) is even in (x,y).

But if you just say "even", rather than "even in (x,y)", then yes I would expect it to be even in all variables present.

 

[wumple]

awesome thank you!