Catalogue Search | MBRL
Are you sure you want to remove the book from the shelf?
{{itemTitle}}
7
result(s) for
"zeta psi"
Sort by:
The Lost Boys of Zeta Psi
The Lost Boys of Zeta Psi takes us inside the secret, amusing, and sometimes mundane world of a California fraternity around 1900. Gleaning history from recent archaeological excavations and from such intriguing sources as oral histories, architecture, and photographs, Laurie A. Wilkie uncovers details of everyday life in the first fraternity at the University of California, Berkeley, and sets this story into the rich social and historical context of West Coast America at the turn of the last century. In particular, Wilkie examines men's coming-of-age experiences in a period when gender roles and relations were undergoing dramatic changes. Her innovative study illuminates shifting notions of masculinity and at the same time reveals new insights about the inner workings of fraternal orders and their role in American society.
eBook
Applications of Euler Sums and Series Involving the Zeta Functions
A very recent article delved into and expanded the four parametric linear Euler sums, revealing that two well-established subjects—Euler sums and series involving the zeta functions—display particular correlations. In this study, we present several closed forms of series involving zeta functions by using formulas for series associated with the zeta functions detailed in the aforementioned paper. Another closed form of series involving Riemann zeta functions is provided by utilizing a known identity for a series of rational functions in the series index, expressed in terms of Gamma functions. Furthermore, we demonstrate a myriad of applications and relationships of series involving the zeta functions and the extended parametric linear Euler sums. These include connections with Wallis’s infinite product formula for π, Mathieu series, Mellin transforms, determinants of Laplacians, certain integrals expressed in terms of Euler sums, representations and evaluations of some integrals, and certain parametric Euler sum identities. The use of Mathematica for various approximation values and certain integral formulas is elaborated upon. Symmetry naturally occurs in Euler sums.
Journal Article
Finite summation formulas involving binomial coefficients, harmonic numbers and generalized harmonic numbers
A variety of identities involving harmonic numbers and generalized harmonic numbers have been investigated since the distant past and involved in a wide range of diverse fields such as analysis of algorithms in computer science, various branches of number theory, elementary particle physics and theoretical physics. Here we show how one can obtain further interesting identities about certain finite series involving binomial coefficients, harmonic numbers and generalized harmonic numbers by applying the usual differential operator to a known identity.
MSC:
11M06, 33B15, 33E20, 11M35, 11M41, 40C15.
Journal Article
EXTENSIONS OF EULER HARMONIC SUMS
Three new closed-form summation formulae involving harmonic numbers are established using simple arguments and they are very general extensions of Euler's famous harmonic sum identity. Some illustrative special cases as well as immediate consequences of the main results are also considered.
Journal Article
Certain relationships among polygamma functions, Riemann zeta function and generalized zeta function
Many useful and interesting properties, identities, and relations for the Riemann zeta function
ζ
(
s
)
and the Hurwitz zeta function
ζ
(
s
,
a
)
have been developed. Here, we aim at giving certain (presumably) new and (potentially) useful relationships among polygamma functions, Riemann zeta function, and generalized zeta function by modifying Chen’s method. We also present a double inequality approximating
ζ
(
2
r
+
1
)
by a more rapidly convergent series.
MSC:
11M06, 33B15, 40A05, 26D07.
Journal Article
Certain integral representations of Stieltjes constants γn
A remarkably large number of integral formulas for the Euler-Mascheroni constant
γ
have been presented. The Stieltjes constants (or generalized Euler-Mascheroni constants)
γ
n
and
γ
0
=
γ
, which arise from the coefficients of the Laurent series expansion of the Riemann zeta function
ζ
(
s
)
at
s
=
1
, have been investigated in various ways, especially for their integral representations. Here we aim at presenting certain integral representations for
γ
n
by choosing to use three known integral representations for the Riemann zeta function
ζ
(
s
)
. Our method used here is similar to those in some earlier works, but our results seem a little simpler. Some relevant connections of some special cases of our results presented here with those in earlier works are also pointed out.
MSC:
11M06, 11M35, 11Y60, 33B15.
Journal Article