Faulhaber's formula (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Faulhaber's formula" in English language version.

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8doi.org

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5semanticscholar.org

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4arxiv.org

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1maa.org

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1stanford.edu

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1uniud.it

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academia.edu

Pietrocola, Giorgio (2017), On polynomials for the calculation of sums of powers of successive integers and Bernoulli numbers deduced from the Pascal's triangle, Academia.edu.

archive.org

John H. Conway, Richard Guy (1996). The Book of Numbers. Springer. p. 107. ISBN 0-387-97993-X.

arxiv.org

Donald E. Knuth (1993). "Johann Faulhaber and sums of powers". Mathematics of Computation. 61 (203): 277–294. arXiv:math.CA/9207222. doi:10.2307/2152953. JSTOR 2152953. The arxiv.org paper has a misprint in the formula for the sum of 11th powers, which was corrected in the printed version. Correct version. Archived 2010-12-01 at the Wayback Machine
Lang, Wolfdieter (2017). "On Sums of Powers of Arithmetic Progressions, and Generalized Stirling, Eulerian and Bernoulli numbers". arXiv:1707.04451 [math.NT].
Kieren MacMillan, Jonathan Sondow (2011). "Proofs of power sum and binomial coefficient congruences via Pascal's identity". American Mathematical Monthly. 118 (6): 549–551. arXiv:1011.0076. doi:10.4169/amer.math.monthly.118.06.549. S2CID 207521003.
Guo, Victor J. W.; Zeng, Jiang (30 August 2005). "A q-Analogue of Faulhaber's Formula for Sums of Powers". The Electronic Journal of Combinatorics. 11 (2). arXiv:math/0501441. Bibcode:2005math......1441G. doi:10.37236/1876. S2CID 10467873.

doi.org

Beery, Janet (2009). "Sum of powers of positive integers". MMA Mathematical Association of America. doi:10.4169/loci003284 (inactive 1 November 2024).{{cite news}}: CS1 maint: DOI inactive as of November 2024 (link)
Donald E. Knuth (1993). "Johann Faulhaber and sums of powers". Mathematics of Computation. 61 (203): 277–294. arXiv:math.CA/9207222. doi:10.2307/2152953. JSTOR 2152953. The arxiv.org paper has a misprint in the formula for the sum of 11th powers, which was corrected in the printed version. Correct version. Archived 2010-12-01 at the Wayback Machine
Edwards, Anthony William Fairbank (1982). "Sums of powers of integers: A little of the History". The Mathematical Gazette. 66 (435): 22–28. doi:10.2307/3617302. JSTOR 3617302. S2CID 125682077.
Derby, Nigel (2015), "A search for sums of powers", The Mathematical Gazette, 99 (546): 416–421, doi:10.1017/mag.2015.77, S2CID 124607378.
Kieren MacMillan, Jonathan Sondow (2011). "Proofs of power sum and binomial coefficient congruences via Pascal's identity". American Mathematical Monthly. 118 (6): 549–551. arXiv:1011.0076. doi:10.4169/amer.math.monthly.118.06.549. S2CID 207521003.
Guo, Victor J. W.; Zeng, Jiang (30 August 2005). "A q-Analogue of Faulhaber's Formula for Sums of Powers". The Electronic Journal of Combinatorics. 11 (2). arXiv:math/0501441. Bibcode:2005math......1441G. doi:10.37236/1876. S2CID 10467873.
Beardon, A. F. (1996). "Sums of Powers of Integers". The American Mathematical Monthly. 103 (3): 201–213. doi:10.1080/00029890.1996.12004725.
Derby, Nigel M. (2019). "The continued search for sums of powers". The Mathematical Gazette. 103 (556): 94–100. doi:10.1017/mag.2019.11.

harvard.edu

ui.adsabs.harvard.edu

Guo, Victor J. W.; Zeng, Jiang (30 August 2005). "A q-Analogue of Faulhaber's Formula for Sums of Powers". The Electronic Journal of Combinatorics. 11 (2). arXiv:math/0501441. Bibcode:2005math......1441G. doi:10.37236/1876. S2CID 10467873.

jstor.org

Donald E. Knuth (1993). "Johann Faulhaber and sums of powers". Mathematics of Computation. 61 (203): 277–294. arXiv:math.CA/9207222. doi:10.2307/2152953. JSTOR 2152953. The arxiv.org paper has a misprint in the formula for the sum of 11th powers, which was corrected in the printed version. Correct version. Archived 2010-12-01 at the Wayback Machine
Edwards, Anthony William Fairbank (1982). "Sums of powers of integers: A little of the History". The Mathematical Gazette. 66 (435): 22–28. doi:10.2307/3617302. JSTOR 3617302. S2CID 125682077.

maa.org

Beery, Janet (2009). "Sum of powers of positive integers". MMA Mathematical Association of America. doi:10.4169/loci003284 (inactive 1 November 2024).{{cite news}}: CS1 maint: DOI inactive as of November 2024 (link)

mathworks.com

blogs.mathworks.com

Gulley, Ned (March 4, 2010), Shure, Loren (ed.), Nicomachus's Theorem, Matlab Central

proquest.com

Derby, Nigel (2015), "A search for sums of powers", The Mathematical Gazette, 99 (546): 416–421, doi:10.1017/mag.2015.77, S2CID 124607378.

psu.edu

citeseerx.ist.psu.edu

Howard, F.T (1994). "Sums of powers of integers via generating functions" (PDF). CiteSeerX 10.1.1.376.4044.

researchgate.net

Tan Si, Do (2017). "Obtaining Easily Sums of Powers on Arithmetic Progressions and Properties of Bernoulli Polynomials by Operator Calculus". Applied Physics Research. 9. Canadian Center of Science and Education. ISSN 1916-9639.

semanticscholar.org

api.semanticscholar.org

Edwards, Anthony William Fairbank (1982). "Sums of powers of integers: A little of the History". The Mathematical Gazette. 66 (435): 22–28. doi:10.2307/3617302. JSTOR 3617302. S2CID 125682077.
Kalman, Dan (1988). "Sums of Powers by matrix method". Semantic scholar. S2CID 2656552.
Derby, Nigel (2015), "A search for sums of powers", The Mathematical Gazette, 99 (546): 416–421, doi:10.1017/mag.2015.77, S2CID 124607378.
Kieren MacMillan, Jonathan Sondow (2011). "Proofs of power sum and binomial coefficient congruences via Pascal's identity". American Mathematical Monthly. 118 (6): 549–551. arXiv:1011.0076. doi:10.4169/amer.math.monthly.118.06.549. S2CID 207521003.
Guo, Victor J. W.; Zeng, Jiang (30 August 2005). "A q-Analogue of Faulhaber's Formula for Sums of Powers". The Electronic Journal of Combinatorics. 11 (2). arXiv:math/0501441. Bibcode:2005math......1441G. doi:10.37236/1876. S2CID 10467873.

stanford.edu

www-cs-faculty.stanford.edu

Donald E. Knuth (1993). "Johann Faulhaber and sums of powers". Mathematics of Computation. 61 (203): 277–294. arXiv:math.CA/9207222. doi:10.2307/2152953. JSTOR 2152953. The arxiv.org paper has a misprint in the formula for the sum of 11th powers, which was corrected in the printed version. Correct version. Archived 2010-12-01 at the Wayback Machine

unikassel.de

Helmes, Gottfried (2006). "Accessing Bernoulli-Numbers by Matrix-Operations" (PDF). Uni-Kassel.de.

uniud.it

users.dimi.uniud.it

Howard, F.T (1994). "Sums of powers of integers via generating functions" (PDF). CiteSeerX 10.1.1.376.4044.

web.archive.org

Donald E. Knuth (1993). "Johann Faulhaber and sums of powers". Mathematics of Computation. 61 (203): 277–294. arXiv:math.CA/9207222. doi:10.2307/2152953. JSTOR 2152953. The arxiv.org paper has a misprint in the formula for the sum of 11th powers, which was corrected in the printed version. Correct version. Archived 2010-12-01 at the Wayback Machine

worldcat.org

search.worldcat.org

Tan Si, Do (2017). "Obtaining Easily Sums of Powers on Arithmetic Progressions and Properties of Bernoulli Polynomials by Operator Calculus". Applied Physics Research. 9. Canadian Center of Science and Education. ISSN 1916-9639.