The Faulhaber Conjecture Resolved Generalization to Powers Sums on Arithmetic Progressions
New Insights into Physical Science Vol.3,
Page 14-23
Abstract
By comparing the formula giving odd powers sums of integers from Bernoulli numbers and the Faulhaber conjecture form of them, we obtain two recurrence relations for calculating the Faulhaber coefficients. Parallelly we search for and obtain the differential operator which transform a powers sum into a Bernoulli polynomial. From this and by changing arguments from z,n into Z=z(z-1), λ=zn+n(n-1/2) we obtain a formula giving powers sums on arithmetic progressions directly from the powers sums on integers.
Keywords:
- Faulhaber conjecture
- powers sums
- arithmetic progression
- Bernoulli polynomials
- Jacobi formula
How to Cite
Si, D. T. (2020). The Faulhaber Conjecture Resolved Generalization to Powers Sums on Arithmetic Progressions. New Insights into Physical Science Vol.3, 14-23. Retrieved from https://stm1.bookpi.org/index.php/nips-v3/article/view/1813
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