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Science Forum Index » Mathematics Forum » nested power series
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| edward |
 Posted: Sat Dec 27, 2003 3:53 am |
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| If we have a power series whwre each summand term is another power series, how can I represent the entire nested series as just one? |
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| José Carlos Santos |
| Posted: Sat Dec 27, 2003 11:12 am |
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edward wrote:
Quote: If we have a power series whwre each summand term is another
power series, how can I represent the entire nested series as just one?
If you have a series a_0 + a_1*z + a_2*z^2 + a_3*z^3 + ... and if z gets
replaced by b_0 + b_1*z + b_2*z^2 + b_3*z^3 + ..., then what you get is
a power series c_0 + c_1*z + c_2*z^2 + c_3*z^3 + ..., where c_p is equal
to the sum of all numbers a_m*b_{n_1}*b_{n_2}*...*b_{n_m} such that
n_1 + n_2 + ... + n_m = p.
I hope that this helps.
Best regards,
Jose Carlos Santos |
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