Bernoulli–Dunkl and Apostol–Euler–Dunkl polynomials with applications to series involving zeros of Bessel functions

Ciaurri, Óscar; Durán, Antonio J.; Pérez, Mario; Malumbres, Juan

doi:10.1016/j.jat.2018.06.001

Cited by 21 publications

(10 citation statements)

References 22 publications

(36 reference statements)

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“…where {j 1,k } are the (positive) zeroes of the Bessel function J 1 (x). The generating function (C.5) may then be obtained as a corollary of the results in the recent paper [55] that proved that…”

Section: Jhep07(2021)085mentioning

confidence: 89%

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BPS Wilson loop in $$ \mathcal{N} $$ = 2 superconformal SU(N) “orientifold” gauge theory and weak-strong coupling interpolation

Beccaria

Dunne

Tseytlin

2021

J. High Energ. Phys.

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We consider the expectation value $$ \left\langle \mathcal{W}\right\rangle $$ W of the circular BPS Wilson loop in $$ \mathcal{N} $$ N = 2 superconformal SU(N) gauge theory containing a vector multiplet coupled to two hypermultiplets in rank-2 symmetric and antisymmetric representations. This theory admits a regular large N expansion, is planar-equivalent to $$ \mathcal{N} $$ N = 4 SYM theory and is expected to be dual to a certain orbifold/orientifold projection of AdS5× S5 superstring theory. On the string theory side $$ \left\langle \mathcal{W}\right\rangle $$ W is represented by the path integral expanded near the same AdS2 minimal surface as in the maximally supersymmetric case. Following the string theory argument in [5], we suggest that as in the $$ \mathcal{N} $$ N = 4 SYM case and in the $$ \mathcal{N} $$ N = 2 SU(N) × SU(N) superconformal quiver theory discussed in [19], the coefficient of the leading non-planar 1/N2 correction in $$ \left\langle \mathcal{W}\right\rangle $$ W should have the universal λ3/2 scaling at large ’t Hooft coupling. We confirm this prediction by starting with the localization matrix model representation for $$ \left\langle \mathcal{W}\right\rangle $$ W . We complement the analytic derivation of the λ3/2 scaling by a numerical high-precision resummation and extrapolation of the weak-coupling expansion using conformal mapping improved Padé analysis.

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Section: Jhep07(2021)085mentioning

confidence: 89%

“…By the same methods, the results in [55] can be used to construct the generating function for the sums ∞ k=1 1 j 2n a,k of inverse negative even powers of zeroes of J a (x).…”

Section: Jhep07(2021)085mentioning

confidence: 99%

BPS Wilson loop in $$ \mathcal{N} $$ = 2 superconformal SU(N) “orientifold” gauge theory and weak-strong coupling interpolation

Beccaria

Dunne

Tseytlin

2021

J. High Energ. Phys.

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“…are all convergent. For instance, b 1 " tr S " dx n f px 1 , x 2 q f px 2 , x 3 q ¨¨¨f px n´1 , x n q f px n , x 1 q, (C.2) By the same methods, the results in [55] can be used to construct the generating function for the sums ř 8…”

Section: B Weak Coupling Expansion Of Tr Mmentioning

confidence: 99%

BPS Wilson loop in $\mathcal N=2$ superconformal $SU(N)$ "orientifold" gauge theory and weak-strong coupling interpolation

Beccaria,

Dunne,

Tseytlin

2021

Preprint

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We consider the expectation value xWy of the circular BPS Wilson loop in N " 2 superconformal SU pN q gauge theory containing a vector multiplet coupled to two hypermultiplets in rank-2 symmetric and antisymmetric representations. This theory admits a regular large N expansion, is planar-equivalent to N " 4 SYM theory and is expected to be dual to a certain orbifold/orientifold projection of AdS 5 ˆS5 superstring theory. On the string theory side xWy is represented by the path integral expanded near the same AdS 2 minimal surface as in the maximally supersymmetric case. Following the string theory argument in arXiv:2007.08512, we suggest that as in the N " 4 SYM case and in the N " 2 SU pN q ˆSU pN q superconformal quiver theory discussed in arXiv:2102.07696, the coefficient of the leading non-planar 1{N 2 correction in xWy should have the universal λ 3{2 scaling at large 't Hooft coupling. We confirm this prediction by starting with the localization matrix model representation for xWy. We complement the analytic derivation of the λ 3{2 scaling by a numerical high-precision resummation and extrapolation of the weak-coupling expansion using conformal mapping improved Padé analysis.

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“…Many authors are currently working on this issue. Authors [8] solve the Apostol-Euler-Dunkl polynomials with applications to series involving zeros of Bessel functions, and author in [9] describe the growth of polynomials outside of a compact set-The Bernstein-Walsh inequality revisited, and further, the authors [10] deal with the approximation and Entropy Numbers of Embeddings Between Approximation Spaces. Many outputs of approximation techniques are widely used in mechanics, economics, mechatronics, robotics [11,12], instrumentation, technology [13,14,15], assembly [16,17], informatics [18,19] etc.…”

Section: Review Of the Literaturementioning

confidence: 99%

The Method of High Accuracy Calculation of Robot Trajectory for the Complex Curves

Lozhkin

Božek

Maiorov

2020

Management Systems in Production Engineering

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The geometric model accuracy is crucial for product design. More complex surfaces are represented by the approximation methods. On the contrary, the approximation methods reduce the design quality. A new alternative calculation method is proposed. The new method can calculate both conical sections and more complex curves. The researcher is able to get an analytical solution and not a sequence of points with the destruction of the object semantics. The new method is based on permutation and other symmetries and should have an origin in the internal properties of the space. The classical method consists of finding transformation parameters for symmetrical conic profiles, however a new procedure for parameters of linear transformations determination was acquired by another method. The main steps of the new method are theoretically presented in the paper. Since a double result is obtained in most stages, the new calculation method is easy to verify. Geometric modeling in the AutoCAD environment is shown briefly. The new calculation method can be used for most complex curves and linear transformations. Theoretical and practical researches are required additionally.

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Bernoulli–Dunkl and Apostol–Euler–Dunkl polynomials with applications to series involving zeros of Bessel functions

Cited by 21 publications

References 22 publications

BPS Wilson loop in $$ \mathcal{N} $$ = 2 superconformal SU(N) “orientifold” gauge theory and weak-strong coupling interpolation

BPS Wilson loop in $$ \mathcal{N} $$ = 2 superconformal SU(N) “orientifold” gauge theory and weak-strong coupling interpolation

BPS Wilson loop in $\mathcal N=2$ superconformal $SU(N)$ "orientifold" gauge theory and weak-strong coupling interpolation

The Method of High Accuracy Calculation of Robot Trajectory for the Complex Curves

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