Faulhaber's formula: 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: |
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: |
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(This is exactly the as than the task [[Faulhaber%27s_triangle#F%C5%8Drmul%C3%A6|Faulhaber's triangle]]) |
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[[File:Fōrmulæ - Faulhaber 01.png]] |
[[File:Fōrmulæ - Faulhaber 01.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. |
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. |
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(This is exactly the as than the task [[Faulhaber%27s_triangle#F%C5%8Drmul%C3%A6|Faulhaber's triangle]]) |
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This function can be used for both symbolic or numeric computation of the polynomial: |
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[[File:Fōrmulæ - Faulhaber 06.png]] |
[[File:Fōrmulæ - Faulhaber 06.png]] |
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