A refinement of Faulhaber%26apos;s theorem concerning sums of powers of natural numbers

作者：Bazso A; Pinter A; Srivastava H M^*

来源：Applied Mathematics Letters, 2012, 25(3): 486-489.

DOI：10.1016/j.aml.2011.09.042

• Sums of powers of natural numbers
• Faulhaber%26apos
• s polynomials
• Bernoulli polynomials and Bernoulli numbers
• Laguerre polynomials
• Decomposition
• Ring of polynomials

In an attempt to present a refinement of Faulhaber%26apos;s theorem concerning sums of powers of natural numbers, the authors investigate and derive all the possible decompositions of the polynomial S(a,b)(k)(x) which is given by %26lt;br%26gt;S(a,b)(k)(x) =b(k) + (a + b)(k) + (2a + b)(k) + ... + (a(x - 1) + b)(k).

• 出版日期2012-3