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## Main Question or Discussion Point

For solving a series solution near a regular singular point with the Frobenius method, why is it that the indices of summation derivatives aren't shifted?

For example, in my textbook and lecture notes

y = [tex]\sum[/tex]A[tex]_{}n[/tex]x[tex]^{}n+r[/tex] from n=0 to infinity

y' = [tex]\sum[/tex](n+r)A[tex]_{}n[/tex]x[tex]^{}n+r-1[/tex] from n=0 to infinity

y'' = [tex]\sum[/tex](n+r)(n+r-1)A[tex]_{}n[/tex]x[tex]^{}n+r-2[/tex] from n=0 to infinity

But shouldn't the index for y' be from n=1 to infinity because it shifts up when you take the derivative of a summation? Shouldn't the index for y'' be from n=2 to infinity?

Thanks.

For example, in my textbook and lecture notes

y = [tex]\sum[/tex]A[tex]_{}n[/tex]x[tex]^{}n+r[/tex] from n=0 to infinity

y' = [tex]\sum[/tex](n+r)A[tex]_{}n[/tex]x[tex]^{}n+r-1[/tex] from n=0 to infinity

y'' = [tex]\sum[/tex](n+r)(n+r-1)A[tex]_{}n[/tex]x[tex]^{}n+r-2[/tex] from n=0 to infinity

But shouldn't the index for y' be from n=1 to infinity because it shifts up when you take the derivative of a summation? Shouldn't the index for y'' be from n=2 to infinity?

Thanks.