Results 1 to 10 of about 106,566 (267)
AppliedMathBased on a recent representation of the psi function due to Guillera and Sondow and independently Boyadzhiev, new closed forms for various series involving harmonic numbers and inverse factorials are derived.
Kunle Adegoke, Robert Frontczak
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Series of Convergence Rate −1/4 Containing Harmonic Numbers
Axioms, 2023 Two general transformations for hypergeometric series are examined by means of the coefficient extraction method. Several interesting closed formulae are shown for infinite series containing harmonic numbers and binomial/multinomial coefficients.
Chunli Li, Wenchang Chu
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The sum of the telescoping series formed by reciprocals of the cubic polynomials with three different negative integer roots [PDF]
Mathematics in Education, Research and Applications, 2020 This paper deals with the sum of a special telescoping series and is a free follow-up to author’s preceding paper. The terms of this series are reciprocals of the cubic polynomial with three different negative integer roots.
Radovan Potůček
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Families of Integrals of Polylogarithmic Functions
Mathematics, 2019 We give an overview of the representation and many connections between integrals of products of polylogarithmic functions and Euler sums. We shall consider polylogarithmic functions with linear, quadratic, and trigonometric arguments, thereby producing ...
Anthony Sofo
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Median Bernoulli Numbers and Ramanujan’s Harmonic Number Expansion
Mathematics, 2022 Ramanujan-type harmonic number expansion was given by many authors. Some of the most well-known are: Hn∼γ+logn−∑k=1∞Bkk·nk, where Bk is the Bernoulli numbers.
Kwang-Wu Chen
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rf acceleration with harmonic number jump
Physical Review Special Topics. Accelerators and Beams, 2006 We have recently considered acceleration of protons and heavy ions in a fixed-field alternating-gradient accelerator with nonscaling lattice and linear field profile.
Alessandro G. Ruggiero
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Certain Hermite–Hadamard Inequalities for Logarithmically Convex Functions with Applications
Mathematics, 2019 In this paper, we discuss various estimates to the right-hand (resp. left-hand) side of the Hermite⁻Hadamard inequality for functions whose absolute values of the second (resp. first) derivatives to positive real powers are log-convex.
Shilpi Jain +3 more
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AppliedMathTwo classes of series involving differences of harmonic numbers and the binomial coefficients C(3n,n) are evaluated in closed form. The classes under consideration are ∑k=0∞H3k+1−Hk(3k+1)3kkkmzkand∑k=0∞H2k−Hk(3k+1)3kkkmzk, where z is a complex number and
Kunle Adegoke, Robert Frontczak
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Multiple Argument Euler Sum Identities
MathematicsWe develop a number of new identities for linear Euler harmonic number sums with multiple argument. Some new examples of even weight linear Euler harmonic sum identities are given.
Anthony Sofo
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Some results on q-harmonic number sums
Advances in Difference Equations, 2018 In this paper, we establish some relations involving q-Euler type sums, q-harmonic numbers and q-polylogarithms. Then, using the relations obtained with the help of q-analog of partial fraction decomposition formula, we develop new closed form ...
Xin Si
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