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Journal of number theory, ISSN 0022-314X, 2009, Volume 129, Issue 4, pp. 908 - 921
For positive integers α 1 , α 2 , … , α r with α r ⩾ 2 , the multiple zeta value or r-fold Euler sum is defined as ζ ( α ) : = ζ ( α 1 , α 2 , … , α r ) = ∑ 1... 
Drinfeld integral | Multiple zeta value | Sum formula | MATHEMATICS | HARMONIC SERIES | EULER SUMS | EXPLICIT EVALUATION
Journal Article
by Eie, MK and Liaw, WC and Ong, YL
The Rocky Mountain journal of mathematics, ISSN 0035-7596, 04/2020, Volume 50, Issue 2, pp. 551 - 558
We evaluate the multiple zeta value zeta(1, {2}(n+1)) or its dual zeta({2}(n),( )3). When n is even, along with stuffle relations already available, it is... 
modified Bell polynomial | MATHEMATICS | multiple zeta-star value | multiple zeta value | Bernoulli polynomial
Journal Article
Journal of Number Theory, ISSN 0022-314X, 2006, Volume 117, Issue 1, pp. 31 - 52
In this paper, we consider two types of extended Euler sums: E p , q ( k ) = ∑ n = 1 ∞ 1 n q ∑ r = 1 kn 1 r p , T p , q ( k ) = ∑ n = 1 ∞ 1 n q ∑ r = 1 ⌊ n / k... 
Zeta function | Euler sum | Bernoulli polynomial | POLYNOMIALS | MATHEMATICS | zeta function | INTEGRAL-REPRESENTATIONS | Computer science
Journal Article
Rocky Mountain Journal of Mathematics, ISSN 0035-7596, 2017, Volume 47, Issue 7, pp. 2107 - 2131
In this paper, we build some variations of multiple zeta values and investigate their relations. Among other things, we prove that Sigma(|alpha| = m+r 1 <= k1... 
Restricted sum formula | Duality theorem | Multiple zeta value | Sum formula | MATHEMATICS | restricted sum formula | sum formula | duality theorem
Journal Article
Packaging Technology and Science, ISSN 0894-3214, 05/2004, Volume 17, Issue 3, pp. 165 - 174
A comparison was made of the effect of different packaging materials on bacterial growth, off‐odour, pH and colour of chicken breast fillets stored at 4°C. For... 
microbiological growth | chicken | packaging material | off‐odour | oxygen transmission rate | Microbiological growth | Chicken | Oxygen transmission rate | Packaging material | Off-odour | QUALITY | FOOD SCIENCE & TECHNOLOGY | off-odour | MODIFIED ATMOSPHERE STORAGE | MEAT | MICROBIOLOGICAL SHELF-LIFE | INGRESS | BEEF | ENGINEERING, MANUFACTURING | CARBON-DIOXIDE | PORK
Journal Article
Journal of Number Theory, ISSN 0022-314X, 08/2013, Volume 133, Issue 8, pp. 2475 - 2495
The classical Euler decomposition theorem expressed a product of two Riemann zeta values in terms of double Euler sums. Such kind of decomposition theorem are... 
Euler sums | Multiple zeta values | Euler decomposition theorem | Shuffle product formula | Drinfeld integrals | MATHEMATICS | VALUES | SUM FORMULA
Journal Article
Transactions of the American Mathematical Society, ISSN 0002-9947, 03/1996, Volume 348, Issue 3, pp. 1117 - 1136
Generalized Bernoulli polynomials were introduced by Shintani in 1976 in order to express the special values at non-positive integers of Dedekind zeta... 
Integers | Numbers | Series convergence | Analytic functions | Real numbers | Paper | Polynomials | Mathematical functions | Coefficients | Vertices | MATHEMATICS
Journal Article
Packaging Technology and Science, ISSN 0894-3214, 01/2004, Volume 17, Issue 1, pp. 43 - 52
A comparison was made of oxygen barrier properties and wall thickness distribution of different thermoformed trays. The thermoformed trays were manufactured... 
thickness | thermoforming | oxygen transmission | drawing depth | Thickness | Oxygen transmission | Drawing depth | Thermoforming | FOOD SCIENCE & TECHNOLOGY | ENGINEERING, MANUFACTURING | LAYERS
Journal Article
American journal of mathematics, ISSN 0002-9327, 8/1998, Volume 120, Issue 4, pp. 811 - 826
We consider the cohomology group associated with Jacobi cusp forms over Cayley numbers as an example of the general theory of the cohomology groups associated... 
Integers | Mathematical theorems | Mathematical integrals | Mathematical functions | Mathematical vectors | Vector spaces | Mathematical congruence | Mathematical cusps | Arithmetic | Cohomology operations | Cayley algebras | Jacobi forms | MATHEMATICS | MAASS SPACE | Congruences and residues | Analysis | Cayley-Hamilton theorem | Representations of groups
Journal Article
International dairy journal, ISSN 0958-6946, 2005, Volume 15, Issue 4, pp. 355 - 362
The oxidative stability of cream cheese stored in thermoformed trays made of amorphous polyethylene terephtalate (A-PET)/polyethylene (PE), polystyrene... 
Cream cheese | Thermoformed tray | Drawing depth | Oxidative stability | Light | OXYGEN | TRANSMISSION | POLYSTYRENE | thermoformed tray | light | MODIFIED ATMOSPHERE | oxidative stability | FOOD SCIENCE & TECHNOLOGY | cream cheese | drawing depth | QUALITY CHANGES | Propylene | Packaging | Aluminum compounds | Polyethylene | Corundum | Ethylene vinyl alcohol
Journal Article
Proceedings of the American Mathematical Society, ISSN 0002-9939, 9/1993, Volume 119, Issue 1, pp. 51 - 61
Let P(X) be a product of k linear forms in r- variables X , ..., X as given by Suppose that β = (β , ..., β ) is an r-tuple of nonnegative integers. Consider... 
Integers | Series convergence | Numbers | Applied mathematics | Finite sums | Polynomials | Mathematical functions | Coefficients | Decreasing functions | MATHEMATICS | ZETA | MATHEMATICS, APPLIED
Journal Article
Computational and Applied Mathematics, ISSN 0101-8205, 2010, Volume 29, Issue 3, pp. 375 - 391
In this paper, we produce shuffle relations from multiple zeta values of the form zeta({1}(m-1,) n + 1). Here {1}(k) is k repetitions of 1, and for a string of... 
Multiple zeta values | Sum formulae | MATHEMATICS, APPLIED | sum formulae | HARMONIC SERIES | multiple zeta values
Journal Article
ITALIAN JOURNAL OF FOOD SCIENCE, ISSN 1120-1770, 2007, Volume 19, pp. 89 - 89
Journal Article
by EIE, MK
MATHEMATISCHE ZEITSCHRIFT, ISSN 0025-5874, 1991, Volume 207, Issue 4, pp. 645 - 655
Journal Article
Italian Journal of Food Science, ISSN 1120-1770, 2007, Volume 19, Issue 2, pp. 127 - 152
Journal Article
by FANG, CH and EIE, MK
PACIFIC JOURNAL OF MATHEMATICS, ISSN 0030-8730, 10/1990, Volume 145, Issue 2, pp. 201 - 210
Journal Article
Transactions of the American Mathematical Society, ISSN 0002-9947, 08/1999, Volume 351, Issue 8, pp. 3217 - 3228
Let \beta =(\beta _{1},\ldots ,\beta _{r}) be an r-tuple of non-negative integers and P_{j}(X) (j=1,2,\ldots ,n) be polynomials in {\mathbb{R}}[X_{1},\ldots... 
Integers | Series convergence | Absolute convergence | Analytic functions | Real numbers | Polynomials | Mathematical functions | Coefficients | Number theory | MATHEMATICS | DIRICHLET
Journal Article
by EIE, MK and KRIEG, A
MATHEMATISCHE ZEITSCHRIFT, ISSN 0025-5874, 05/1992, Volume 210, Issue 1, pp. 113 - 128
Journal Article
Proceedings of the American Mathematical Society, ISSN 0002-9939, 11/1990, Volume 110, Issue 3, pp. 583 - 590
Let be a polynomial with real coefficients and . Define the zeta function Z (s) associated with the polynomial P(x) as Z (s) is holomorphic for and it has an... 
Integers | Mathematical theorems | Absolute convergence | Mathematical functions | Polynomials | Coefficients | College mathematics | MATHEMATICS | MATHEMATICS, APPLIED
Journal Article
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