Faulhaber's triangle: Difference between revisions

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The following function creates the Faulhaber's coefficients up to a given number of rows, according to the [http://www.ww.ingeniousmathstat.org/sites/default/files/Torabi-Dashti-CMJ-2011.pdf paper] of of Mohammad Torabi Dashti:

(This is exactly the same as the task [[Faulhaber%27s_formula#F%C5%8Drmul%C3%A6|Faulhaber's formula]])

[[File:Fōrmulæ - Faulhaber 01.png]]

'''~~Task~~ 1.''' To show the first 11 rows (the first is the 0 row) of Faulhaber's triangle:

'''Excecise 1.''' To show the first 11 rows (the first is the 0 row) of Faulhaber's triangle:

[[File:Fōrmulæ - Faulhaber 02.png]]

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Notes. The -1 index means the last element (-2 is the penultimate element, and so on). So it retrieves the last row of the triangle. |x| is the cardinality (number of elements) of x.

(This is exactly the same as the task [[Faulhaber%27s_formula#F%C5%8Drmul%C3%A6|Faulhaber's formula]])

This function can be used for both symbolic or numeric computation of the polynomial:

[[File:Fōrmulæ - Faulhaber 06.png]]

'''~~Task~~ 2.''' Using the 18th row of Faulhaber's triangle, compute the sum <math>\sum_{k=1}^{1000} k^{17}</math>

'''Excecise 2.''' Using the 18th row of Faulhaber's triangle, compute the sum <math>\sum_{k=1}^{1000} k^{17}</math>

[[File:Fōrmulæ - Faulhaber 09.png]]