I am struggling to see how P_{k}(x)= [1/(2^{k}(k!))][(d^{k}((x^{2}-1)^{k})/dx^{k}] = [1/(2^{k})][2k choose k][x^{k}] + (terms of lower order) Help please?
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is a polynomial of degree ; when you take the -th derivative it's a polynomial of degree . Now, look at the leading term.
Thank you - a great help!
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