Some closed-form evaluations of infinite products involving nested radicals

Asymptotic Behaviour of Some Infinite Products Involving Prime Numbers

Asymptotic behaviour of some infinite products involving prime numbers

The asymptotic behaviour of some entire functions defined via infinite products is investigated as the parameter z tends to infinity in the sector | arg z| < π. These functions arise in the distributions of the number of prime factors of integers and of the number of irreducible factors of monic polynomials over a finite field. Our approach is based on the Mellin transform with a suitable conto...

Closed-form sums for some perturbation series involving hypergeometric functions

Infinite series of the type ∞ ∑ n=1 ( 2 )n n 1 n! 2F1(−n, b; γ; y) are investigated. Closed-form sums are obtained for α a positive integer α = 1, 2, 3, . . . . The limiting case of b → ∞, after y is replaced with x2/b, leads to ∞ ∑ n=1 ( 2 )n n 1 n! 1F1(−n, γ, x2). This type of series appears in the first-order perturbation correction for the wavefunction of the generalized spiked harmonic osc...

Closed Form of Infinite Series Used in Some Atomic Integrals Containing r12, r13, and r23

Articles you may be interested in Atomic Integrals Containing r23 λ r31 μ r12 v

Closed-form Summation of Some Trigonometric Series

The problem of numerical evaluation of the classical trigonometric series ^ sin(2fr+ l)a . ^ cOS(2/c + l)a ¿„(a) = > ——;-—— ana C„(a) = > —rr-,-t;—» £j (2k+1)" ÍTo Vk+XY where v > 1 in the case of Sin(a) and C2„+X(a) with n = 1, 2, 3, ... has been recently addressed by Dempsey, Liu, and Dempsey; Boersma and Dempsey; and by Gautschi. We show that, when a is equal to a rational multiple of 2k , t...