We present a method for calculating any (nested) harmonic sum to arbitrary accuracy for all complex values of the argument. The method utilizes the relation between harmonic sums and (derivatives of) Hurwitz zeta functions, which allows a harmonic sum to be calculated as an expansion valid for ...
The sum-frequency generation from a multi-resonant nanoantenna (MR-NA) and the second-harmonic generation from a particle-in-cavity nanoantenna (PIC-NA) are analyzed by using the developed method. Enhancements of the scattering signals due to double-resonance of the multi-resonant nanoantenna and ...
Sum Geometric Harmonic Means Index of Graphsdoi:10.56807/buj.v5i4.468Mahde, Sultan SenanAbdallah, Ebrahim MohammedAlbaydaa University Journal
In this study, simultaneous second-harmonic generation (SHG), sum frequency generation (SFG), and Raman conversion based on MgO-doped periodically poled lithium niobate (MgO:PPLN) for multi-wavelength generation is demonstrated. The approach used is based on a single MgO:PPLN crystal poled with ...
sum = log(n) + x +1.0/(2*n); #include <bits/stdc++.h>#defineios ios::sync_with_stdio(false)#definemid (l+r)/2#definell long longusingnamespacestd;doublearr[100100];intmain(){doublex =0.57721566490153286060651209;intpos =0, t, n;doubleans =1, sum;for(inti =1; i <=100000;...
\frac{1}{2}H_n=\frac{1}{2}\sum_{k=1}^n\frac{1}{k} 当n\rightarrow\infty时,这就是调和级数的一半,结果发散,且重心位置的极限是最底层骨牌的最左端,但最顶层骨牌与最底层骨牌的距离会趋于无穷。 六、回首引子二 这道解析题目涉及到了前文中没有提到过的“调和”家族的新成员——调和点列。
We derived the sum identities for generalized harmonic and corresponding oscillatory numbers for which a sieve procedure can be applied. The obtained resul... RM Abrarov,SM Abrarov - 《Mathematics》 被引量: 1发表: 2012年 Criteria for Irrationality of Euler's Constant Prime Number TheoremBy modif...
In this paper a method is presented for modeling the observed frequency spectrum of a rapidly oscillating Ap star as a sum of axisymmetric spherical harmonics of low degree within the assumptions of the oblique pulsator model. It is shown that such a sum with l not greater than 3 is ...
We show how infinite series of a certain type involving generalized harmonic numbers can be computed using a knowledge of symmetric functions and multiple zeta values. In particular, we prove and generalize some identities recently conjectured by J. Choi, and give several more families of identities...
Harmonic numbers H_k=\\sum_{03 p>3 we have \\sum_{k=1}^{p-1}H_k/(k2^k)=7/24*pB_{p-5} (mod p^2) \\sum_{k=1}^{p-1}H_k/(k2^k)=7/24*pB_{p-5} (mod p^2) and \\... ZW Sun,ZW Sun,LL Zhao 被引量: 0发表: 2009年 Proc. Amer. Math. Soc. 140(2012)...