Transcendental Infinite Sums and Some Related Questions

2002 ◽  
pp. 169-178
Author(s):  
Sukumar Das Adhikari
Keyword(s):  
Infinite Sums

Mixing for stationary processes with finite-order multiple Wiener-Itô integral representation

1996 ◽  
Vol 16 (5) ◽  
pp. 1087-1100
Author(s):  
Eric Slud ◽  
Daniel Chambers
Keyword(s):  
Large Class ◽  
Order Term ◽  
Sufficient Conditions ◽  
Polynomial Form ◽  
Itô Integral ◽  
Ito Integral ◽  
Weakly Mixing ◽  
Subordinated Processes ◽  
Infinite Sums ◽  
Necessary And Sufficient

abstractNecessary and sufficient analytical conditions are given for homogeneous multiple Wiener-Itô integral processes (MWIs) to be mixing, and sufficient conditions are given for mixing of general square-integrable Gaussian-subordinated processes. It is shown that every finite or infinite sum Y of MWIs (i.e. every real square-integrable stationary polynomial form in the variables of an underlying weakly mixing Gaussian process) is mixing if the process defined separately by each homogeneous-order term is mixing, and that this condition is necessary for a large class of Gaussian-subordinated processes. Moreover, for homogeneous MWIs Y1, for sums of MWIs of order ≤ 3, and for a large class of square-integrable infinite sums Y1, of MWIs, mixing holds if and only if Y2 has correlation-function decaying to zero for large lags. Several examples of the criteria for mixing are given, including a second-order homogeneous MWI, i.e. a degree two polynomial form, orthogonal to all linear forms, which has auto-correlations tending to zero for large lags but is not mixing.

Infinite sums in totally ordered abelian groups

2019 ◽  
Vol 12 (2) ◽  
pp. 281-300
Author(s):  
Greg Oman ◽  
Caitlin Randall ◽  
Logan Robinson
Keyword(s):  
Abelian Groups ◽  
Infinite Sums

On finite and infinite sums of the form Σ P(x)/Kx

1964 ◽  
Vol 52 (6) ◽  
pp. 725-725
Author(s):  
R.E. Allan
Keyword(s):  
Infinite Sums

Applications of Infinite Sums and Products

1999 ◽  
pp. 117-122
Author(s):  
Steven G. Krantz
Keyword(s):  
Infinite Sums

scholarly journals Some new sums of q-trigonometric and related functions through a theta product of Jacobi

2020 ◽  
Vol 16 (08) ◽  
pp. 1803-1817
Author(s):  
Mohamed El Bachraoui ◽  
József Sándor
Keyword(s):  
Product Formula ◽  
Infinite Sums ◽  
Trigonometric Identities

We evaluate some finite and infinite sums involving [Formula: see text]-trigonometric and [Formula: see text]-digamma functions. Upon letting [Formula: see text] approach [Formula: see text], one obtains corresponding sums for the classical trigonometric and the digamma functions. Our key argument is a theta product formula of Jacobi and Gosper’s [Formula: see text]-trigonometric identities.

scholarly journals On certain maps defined by infinite sums

2020 ◽  
Vol 28 (4) ◽  
pp. 987-1007
Author(s):  
Symon Serbenyuk
Keyword(s):  
Infinite Sums

Über reihen auf der convergenzgrenze

1900 ◽  
Vol 66 (424-433) ◽  
pp. 337-339
Keyword(s):  
Multiple Integration ◽  
The Subject ◽  
Infinite Sums

The essay is divided into three chapters. A limit operation of any kind, for instance, simple or multiple integration; the formation of infinite sums or products; or any combination of these operations gives rise to certain typical considerations which form the subject of the first chapter.

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