We study the sum of the finite multiple harmonic q-series on r-(r + 1) indices at roots of unity with r = 1, 2, 3. Mainly, we give equivalent conditions of two conjectures regarding cyclic sums of finite multiple harmonic q-series on 1-2-3 indices at roots of unity, posed ...
Forn→ ∞, the quantity (a1rn)/ (1 -r) → 0 for -1.0 < (r≠ 0) < +1.0, thus, S=a11−rS=a11−r See also the derivation for theproduct of GP. Tags Algebra Derivation of Formula Progression sequence series Geometric Progression ...
An infinite series is the sum of terms in an infinitely long sequence, but taking the sum of terms in a finite portion of the sequence is called a partial sum. Explore these two concepts through examples of five types of series: arithmetic, geometric, harmonic, alternating...
We define two finite q-analogs of certain multiple harmonic series with an arbitrary number of free parameters, and prove identities for these q-analogs, e... NW Yasuo Ohno 被引量: 67发表: 2006年 A q-analog of Euler's decomposition formula for the double zeta function The double zeta fun...
1.The Series sum from n=1 to ∞(x~n) Applies in Solving Summation Function and Summation of Series关于幂级数在求和函数及级数求和方面的应用 2.The formula of finite summation of K Steps arithmetic progression is seeked out by using the summation function of power series.用幂级数和函数的思想来...
An infinite series is the sum of terms in an infinitely long sequence, but taking the sum of terms in a finite portion of the sequence is called a partial sum. Explore these two concepts through examples of five types of series: arithmetic, geometric, har...
An infinite series is the sum of terms in an infinitely long sequence, but taking the sum of terms in a finite portion of the sequence is called a partial sum. Explore these two concepts through examples of five types of series: a...
In the long-distance limit, the partition function is given as a finite sum over the contributions of the discrete massive vacua of the resulting N=1 theory. In the case at hand, it turns that, for G = SU(N), the number of such vacua is given by the sum of the positive divisors ...
Reference [36] introduces a novel approach for multiple source DOA estimation using the maximum likelihood method in the spherical harmonic domain. By employing an efficient sequential iterative search of maxima on the cost function, the proposed method achieves superior performance compared to traditional...
If |n)=∑α|n,α〉, in which |n,0〉 is the harmonic state vector, then (n|f|n+k)=∑ℓ∑(s)ℓ2−ℓ/2ℓ!fs1s2⋯sr(ℓ)∑αβ〈n,α|ξ1s1ξ2s2⋯ξrsr|n+k,β〉. Having used the polynomial definition (3.5), we derive the formula (n|f|n+k)=gn,n+k∑...