5 ms·
Integrate the constant 48 back to the series level: 48 -> 48x -> 24x^2 -> 8x^3 Subtract 8x^3 from the series 9 - 8•1^3, 73 - 8•2^3, 241 - 8•3^3 and repe
by jonsen 17y ago
Integrate the constant 48 back to the series level:
48 -> 48x -> 24x^2 -> 8x^3
Subtract 8x^3 from the series
9 - 8•1^3, 73 - 8•2^3, 241 - 8•3^3
and repeat the whole process on this series for the coefficient of x^2, etc...
- SandB0x 17y agoExactly. The other perspective: When you see 'difference', think 'derivative' . Approximately, what the difference table is doing is differentiating until the leading term is constant. If we end up with a constant k levels down, we must have had a.x^k in the polynomial, as the derivative of a.x^k = ak.x^(k-1). Repeating this k times gives constant = a.k! So the leading coefficient of the polynomial, a = constant/k! I guess the next step is to subtract the values generated by this term from the sequence, then repeat to find the next term in the polynomial...