Harmonic series with polygamma functions
نویسندگان
چکیده
منابع مشابه
Series associated with Polygamma functions
We use integral identities to establish a relationship with sums that include polygamma functions, moreover we obtain some closed forms of binomial sums. In particular cases, we establish some identities for Polygamma functions
متن کاملInequalities for the polygamma functions with application
We present some inequalities for the polygamma functions. As an application, we give the upper and lower bounds for the expression n ∑ k=1 1 k − lnn− γ, where γ = 0.57721... is the Euler’s constant. 2000 Mathematics Subject Classification: 26D15, 33B15.
متن کاملPolyGamma Functions of Negative Order
Liouville's fractional integration is used to de ne polygamma functions (z) for negative integer n. It's shown that such (z) can be represented in a closed form by means of the rst derivatives of the Hurwitz Zeta function. Relations to the Barnes G-function and generalized Glaisher's constants are also discussed.
متن کاملSharp Inequalities for Polygamma Functions
where μ is a nonnegative measure on [0,∞) such that the integral (2) converges for all x > 0. This means that a function f(x) is completely monotonic on (0,∞) if and only if it is a Laplace transform of the measure μ. The completely monotonic functions have applications in different branches of mathematical sciences. For example, they play some role in combinatorics, numerical and asymptotic an...
متن کاملSums in Terms of Polygamma Functions
We consider sums involving the product of reciprocal binomial coefficient and polynomial terms and develop some double integral identities. In particular cases it is possible to express the sums in closed form, give some general results, recover some known results in Coffey [8] and produce new identities.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Classical Analysis
سال: 2016
ISSN: 1848-5987
DOI: 10.7153/jca-08-11