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The series for exp(x) is 1+x+x2/2!+x3/3!+x4/4!+x5/5!+... . But as a practical matter if you want to compute a partial sum you wouldn't evaluate it as written. You could use Horner's method, aka synthetic division, but as stated in our article it would rewrite the first 6 terms as 1+x(1+x(1/2!+x(1/3!+x(1/4!+x/5!)))). This reduces the number of multiplications but you'd still need to compute the factorials. It seems easier to factor out those multiplications as well, giving 1+x(1+(x/2)(1+(x/3)(1+(x/4)(1+x/5)))). Horner's method doesn't quite seem to fit, so is there a different name for this type of expansion? They can be used for other partials sums as well. For example (1-4x)-1/2≈1+2x(1+(6x/2)(1+(10x/3)(1+(14x/4)(1+18x/5)))), π/2≈1+(1/3)(1+(2/5)(1+(3/7)(1+(4/9)(1+5/11)))). -- RDBury ( talk) 09:03, 16 July 2023 (UTC)
Do you agree? ( more unambiguously) Hildeoc ( talk) 20:00, 16 July 2023 (UTC)
Mathematics desk | ||
---|---|---|
< July 15 | << Jun | July | Aug >> | July 17 > |
Welcome to the Wikipedia Mathematics Reference Desk Archives |
---|
The page you are currently viewing is a transcluded archive page. While you can leave answers for any questions shown below, please ask new questions on one of the current reference desk pages. |
The series for exp(x) is 1+x+x2/2!+x3/3!+x4/4!+x5/5!+... . But as a practical matter if you want to compute a partial sum you wouldn't evaluate it as written. You could use Horner's method, aka synthetic division, but as stated in our article it would rewrite the first 6 terms as 1+x(1+x(1/2!+x(1/3!+x(1/4!+x/5!)))). This reduces the number of multiplications but you'd still need to compute the factorials. It seems easier to factor out those multiplications as well, giving 1+x(1+(x/2)(1+(x/3)(1+(x/4)(1+x/5)))). Horner's method doesn't quite seem to fit, so is there a different name for this type of expansion? They can be used for other partials sums as well. For example (1-4x)-1/2≈1+2x(1+(6x/2)(1+(10x/3)(1+(14x/4)(1+18x/5)))), π/2≈1+(1/3)(1+(2/5)(1+(3/7)(1+(4/9)(1+5/11)))). -- RDBury ( talk) 09:03, 16 July 2023 (UTC)
Do you agree? ( more unambiguously) Hildeoc ( talk) 20:00, 16 July 2023 (UTC)