Formatting problem or new notation?

Unless you are using a notation completely unknown to me, I cannot tell exactly what you mean from your message below:

P₁(x)=x, P_{2n}(x)=(x+1)P_{2n-1}(x)+x, P_{2n+1}(x)=(x+1)P_{2n}(x)

The "_{...}" in particlular is new to me.

I am used to seeing polynomials using subscript index numbers for coefficients or functions, and superscript for exponents. I have never seen underscore followed by braces and have no idea what it may mean.

Do you mean "P sub 2n times x" or "P sub 2n of x" ?

Bye.