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searching for Sums of powers 34 found (51 total)

Faulhaber's formula (8,109 words) [view diff] exact match in snippet view article find links to article

(1994). "Sums of powers of integers via generating functions" (PDF). CiteSeerX 10.1.1.376.4044. Lang, Wolfdieter (2017). "On Sums of Powers of Arithmetic

Waring–Goldbach problem (395 words) [view diff] exact match in snippet view article find links to article

representation of integers as sums of powers of prime numbers. It is named as a combination of Waring's problem on sums of powers of integers, and the Goldbach

Evil number (326 words) [view diff] exact match in snippet view article find links to article

to the Prouhet–Tarry–Escott problem of finding sets of numbers whose sums of powers are equal up to the k {\displaystyle k} th power. In computer science

List of mathematical series (5,205 words) [view diff] no match in snippet view article find links to article

This list of mathematical series contains formulae for finite and infinite sums. It can be used in conjunction with other tools for evaluating sums. Here

Lieb–Thirring inequality (2,826 words) [view diff] exact match in snippet view article find links to article

and physics, Lieb–Thirring inequalities provide an upper bound on the sums of powers of the negative eigenvalues of a Schrödinger operator in terms of integrals

Lawrence C. Washington (481 words) [view diff] exact match in snippet view article find links to article

Ferrero-Washington). More recently, Washington has published on arithmetic dynamics, sums of powers of primes, and Iwasawa invariants of non-cyclotomic Zp extensions Introduction

Splitting circle method (2,184 words) [view diff] exact match in snippet view article find links to article

elementary symmetric polynomials of a tuple of complex numbers and its sums of powers. Therefore, it is possible to compute the coefficients of a polynomial

List of mathematical functions (1,065 words) [view diff] exact match in snippet view article find links to article

Absolute value: distance to the origin (zero point) Sigma function: Sums of powers of divisors of a given natural number. Euler's totient function: Number

Arithmetic progression (2,297 words) [view diff] exact match in snippet view article find links to article

involving arithmetic progressions Utonality Polynomials calculating sums of powers of arithmetic progressions Hayes, Brian (2006). "Gauss's Day of Reckoning"

Squared triangular number (1,867 words) [view diff] exact match in snippet view article find links to article

and Leibniz, Part III (PDF), AP Central. Edmonds, Sheila M. (1957), "Sums of powers of the natural numbers", The Mathematical Gazette, 41 (337): 187–188

Square pyramidal number (2,316 words) [view diff] exact match in snippet view article find links to article

equation for a sum of squares is a special case of Faulhaber's formula for sums of powers, and may be proved by mathematical induction. More generally, figurate

Goldbach's conjecture (3,720 words) [view diff] exact match in snippet view article find links to article

squares. See Waring's problem and the related Waring–Goldbach problem on sums of powers of primes. Hardy and Littlewood listed as their Conjecture I: "Every

John Horton Conway (3,411 words) [view diff] exact match in snippet view article find links to article

of brickwork patterns in Princeton, lecturing on the ordinals and on sums of powers and the Bernoulli numbers necrology by Keith Hartnett in Quanta Magazine

Closing the Gap: The Quest to Understand Prime Numbers (619 words) [view diff] exact match in snippet view article find links to article

two primes, sums of squares and Waring's problem on representation by sums of powers, the Hardy–Littlewood circle method for comparing the area of a circle

Bruce Reznick (796 words) [view diff] exact match in snippet view article find links to article

systematic analysis of the representation of real forms of even degree as sums of powers of linear forms. This work was described in his monograph Sum of Even

Mathematical Excursions (432 words) [view diff] exact match in snippet view article find links to article

on geometry. Its topics include squared triangular numbers and other sums of powers, Russian peasant multiplication, binary numbers, repeating decimals

Summation by parts (2,162 words) [view diff] exact match in snippet view article find links to article

490–514. doi:10.1016/j.aam.2007.02.001. Edmonds, Sheila M. (1957). "Sums of powers of the natural numbers". The Mathematical Gazette. 41 (337): 187–188

Neuman–Sándor mean (557 words) [view diff] exact match in snippet view article find links to article

2012. doi:10.1155/2012/302635 E. Neuman, Inequalities for weighted sums of powers and their applications, Math. Inequal. Appl. 15 (2012), No. 4, 995–1005

Calkin–Wilf tree (1,949 words) [view diff] exact match in snippet view article find links to article

Lind. However, Carlitz's paper describes a more restricted class of sums of powers of two, counted by fusc(n) instead of by fusc(n + 1). Bates, Bunder

Binomial theorem (6,735 words) [view diff] exact match in snippet view article find links to article

Stirling's approximation Tannery's theorem Polynomials calculating sums of powers of arithmetic progressions q-binomial theorem This is to guarantee convergence

Waring's problem (3,102 words) [view diff] exact match in snippet view article find links to article

numbers Waring–Goldbach problem, the problem of representing numbers as sums of powers of primes Subset sum problem, an algorithmic problem that can be used

Victoria Powers (754 words) [view diff] exact match in snippet view article find links to article

fields", J. Algebra, vol. 136, no.1, 51-59. 1996 (with Eberhard Becker) "Sums of powers in rings and the real holomorphy ring", J. Reine Angew. Math., vol 480

Eisenstein series (3,533 words) [view diff] exact match in snippet view article find links to article

series given above, they may be restated as identities involving the sums of powers of divisors: ( 1 + 240 ∑ n = 1 ∞ σ 3 ( n ) q n ) 2 = 1 + 480 ∑ n = 1

Outline of discrete mathematics (1,833 words) [view diff] exact match in snippet view article find links to article

secure communication techniques Faulhaber's formula – Expression for sums of powers Binary relation – Relationship between elements of two sets Heterogeneous

Thue–Morse sequence (3,873 words) [view diff] exact match in snippet view article find links to article

1, ..., N-1 } into two disjoint subsets S0 and S1 that have equal sums of powers up to k, that is: ∑ x ∈ S 0 x i = ∑ x ∈ S 1 x i {\displaystyle \sum

Pascal's triangle (7,606 words) [view diff] exact match in snippet view article find links to article

theorem Trinomial expansion Trinomial triangle Polynomials calculating sums of powers of arithmetic progressions Coolidge, J. L. (1949), "The story of the

Bernoulli polynomials (4,328 words) [view diff] exact match in snippet view article find links to article

polynomials of the second kind Stirling polynomial Polynomials calculating sums of powers of arithmetic progressions Hurtado Benavides, Miguel Ángel. (2020).

Hurwitz zeta function (4,190 words) [view diff] exact match in snippet view article find links to article

arbitrary s. See also Faulhaber's formula for a similar relation on finite sums of powers of integers. The Laurent series expansion can be used to define generalized

Abc conjecture (4,588 words) [view diff] exact match in snippet view article find links to article

generalization of Fermat's Last Theorem concerning powers that are sums of powers. The L-function L(s, χd) formed with the Legendre symbol, has no Siegel

Coin problem (3,743 words) [view diff] exact match in snippet view article find links to article

MathWorld. Tuenter, Hans J. H. (April 2006). "The Frobenius problem, sums of powers of integers, and recurrences for the Bernoulli numbers". Journal of

Shayle R. Searle (3,294 words) [view diff] exact match in snippet view article find links to article

JSTOR 2681294. Searle, SR (1968). "A remark on solving equations in sums of powers". Journal of the Royal Statistical Society, Series B. 30 (3): 567–569

Algorithms for calculating variance (5,769 words) [view diff] exact match in snippet view article find links to article

A}}{n_{X}}}\end{aligned}}} Here the M k {\displaystyle M_{k}} are again the sums of powers of differences from the mean ∑ ( x − x ¯ ) k {\textstyle \sum (x-{\overline

Vladimir Pletser (4,296 words) [view diff] exact match in snippet view article find links to article

pursuing research in Number Theory, on Generalised Mersenne numbers, on sums of powers of consecutive integers, on multiple of triangular numbers, on characteristics

Generating function transformation (11,140 words) [view diff] exact match in snippet view article find links to article

G-function, combinatorial sums involving the double factorial function, sums of powers sequences, and sequences of binomials. For fixed k ∈ Z + {\displaystyle