Sadri Hassani. Mathematical Methods for Students of Physics and Related Fields, 2nd edition. Springer


Chapter 5. Dirac Delta Function


문제 5.15 및 솔루션



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어렵네요


https://mathworld.wolfram.com/LatticeSum.html

Lattice Sum -- from Wolfram MathWorld

Cubic lattice sums include the following: b_2(2s) = sum^'_(i,j=-infty)^infty((-1)^(i+j))/((i^2+j^2)^s) (1) b_3(2s) = sum^'_(i,j,k=-infty)^infty((-1)^(i+j+k))/((i^2+j^2+k^2)^s) (2) b_n(2s) = sum^'_(k_1,...,k_n=-infty)^infty((-1)^(k_1+...+k_n))/((k_1^2+...+k_n^2)^s), (3) where the prime indicates that the origin (0,0), (0,0,0), etc. is excluded from the sum (Borwein and Borwein 1986, p. 288). These have closed forms for even n, b_2(2s) = -4beta(s)eta(s) (4) b_4(2s) = -8eta(s)eta(s-1) (5) ...

mathworld.wolfram.com