Odd/even for a multivariable function

AI Thread Summary
The standard definition of an odd function in multiple variables is f(-x, -y) = -f(x, y). Some functions can be categorized as odd or even only in a specific set of variables while being parametrized by others. For example, a family of even functions of x and y, parametrized by z, can be expressed as F(x, y; z) where F(-x, -y; z) = F(x, y; z) holds true for all values of z. It's important to specify the variables when discussing evenness or oddness to avoid confusion. Overall, clarity in variable specification is crucial in defining the properties of multivariable functions.
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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!
 
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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.
 
awesome thank you!
 
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