Erratum to “A theorem for the closed-form evaluation of the first generalized Stieltjes constant at rational arguments and some related summations” [J. Number Theory 148 (2015) 537–592]

International audience In a companion paper, ``On multi Hurwitz-zeta function values at rational arguments, Acta Arith. {\bf 107} (2003), 45-67'', we obtained a closed form evaluation of Ramanujan's type of the values of the (multiple) Hurwitz zeta-function at rational arguments (with denominator even and numerator odd), which was in turn a vast generalization of D. Klusch's and M. Katsurada's generalization of Ramanujan's formula. In this paper we shall continue our pursuit, specializing to the Riemann zeta-function, and obtain a closed form evaluation thereof at all rational arguments, with no restriction to the form of the rationals, in the critical strip. This is a complete generalization of the results of the aforementioned two authors. We shall obtain as a byproduct some curious identities among the Riemann zeta-values.

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Closed form evaluation of sums containing squares of Fibonomial coefficients

Mathematica Slovaca ◽

10.1515/ms-2015-0177 ◽

2016 ◽

Vol 66 (3) ◽

Cited By ~ 2

Author(s):

Emrah Kiliç ◽

Helmut Prodinger

Keyword(s):

Closed Form ◽

Systematic Approach ◽

Sums Of Squares ◽

Lucas Numbers ◽

Fibonomial Coefficients ◽

Finite Products ◽

Fibonacci And Lucas Numbers ◽

Form Evaluation

AbstractWe give a systematic approach to compute certain sums of squares of Fibonomial coefficients with finite products of generalized Fibonacci and Lucas numbers as coefficients. The technique is to rewrite everything in terms of a variable

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CLOSED FORMS FOR DEGENERATE BERNOULLI POLYNOMIALS

Bulletin of the Australian Mathematical Society ◽

10.1017/s0004972719001266 ◽

2020 ◽

Vol 101 (2) ◽

pp. 207-217 ◽

Cited By ~ 1

Author(s):

LEI DAI ◽

HAO PAN

Keyword(s):

Number Theory ◽

Closed Form ◽

Bernoulli Polynomials ◽

Stirling Numbers ◽

Closed Form Expression ◽

Form Expression

Qi and Chapman [‘Two closed forms for the Bernoulli polynomials’, J. Number Theory159 (2016), 89–100] gave a closed form expression for the Bernoulli polynomials as polynomials with coefficients involving Stirling numbers of the second kind. We extend the formula to the degenerate Bernoulli polynomials, replacing the Stirling numbers by degenerate Stirling numbers of the second kind.

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On a family of logarithmic and exponential integrals occurring in probability and reliability theory

The Journal of the Australian Mathematical Society Series B Applied Mathematics ◽

10.1017/s0334270000009553 ◽

1994 ◽

Vol 35 (4) ◽

pp. 469-478 ◽

Cited By ~ 2

Author(s):

M. Aslam Chaudhry

Keyword(s):

Closed Form ◽

Recurrence Relation ◽

Reliability Theory ◽

Integral Function ◽

Integral Representations ◽

Exponential Integral ◽

Error Functions ◽

Special Cases ◽

Image Position ◽

Form Evaluation

AbstractWe define an integral function Iμ(α, x; a, b) for non-negative integral values of μ byIt is proved that Iμ(α, x; a, b) satisfies a functional recurrence relation which is exploited to find a closed form evaluation of some incomplete integrals. New integral representations of the exponential integral and complementary error functions are found as special cases.

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