Generalized integrals of Macdonald and Gegenbauer functions

Publikation: Working paper › Preprint › Forskning

Standard

Generalized integrals of Macdonald and Gegenbauer functions. / Dereziński, Jan; Gaß, Christian; Ruba, Błażej.

arXiv.org, 2023.

Publikation: Working paper › Preprint › Forskning

Harvard

Dereziński, J, Gaß, C & Ruba, B 2023 'Generalized integrals of Macdonald and Gegenbauer functions' arXiv.org.

APA

Dereziński, J., Gaß, C., & Ruba, B. (2023). Generalized integrals of Macdonald and Gegenbauer functions. arXiv.org.

Vancouver

Dereziński J, Gaß C, Ruba B. Generalized integrals of Macdonald and Gegenbauer functions. arXiv.org. 2023 apr. 12.

Author

Dereziński, Jan ; Gaß, Christian ; Ruba, Błażej. / Generalized integrals of Macdonald and Gegenbauer functions. arXiv.org, 2023.

Bibtex

@techreport{35b2e713461442dc9c60f7b2ca8b460f,
title = "Generalized integrals of Macdonald and Gegenbauer functions",
abstract = " We compute bilinear integrals involving Macdonald and Gegenbauer functions. These integrals are convergent only for a limited range of parameters. However, when one uses generalized integrals they can be computed essentially without restricting the parameters. The generalized integral is a linear functional extending the standard integral to a certain class of functions involving finitely many homogeneous non-integrable terms at the edpoints of the interval. For generic values of parameters, generalized bilinear integrals of Macdonald and Gegenbauer functions can be obtained by analytic continuation from the region in which the integrals are convergent. In the case of integer parameters we obtain expressions with explicit additional terms related to an anomaly, namely the failure of the generalized integral to be scaling invariant. ",
keywords = "math.CA, math-ph, math.MP, 33C05, 33C10, 47A52",
author = "Jan Derezi{\'n}ski and Christian Ga{\ss} and B{\l}a{\.z}ej Ruba",
note = "39 pages",
year = "2023",
month = apr,
day = "12",
language = "English",
publisher = "arXiv.org",
type = "WorkingPaper",
institution = "arXiv.org",

}

RIS

TY - UNPB

T1 - Generalized integrals of Macdonald and Gegenbauer functions

AU - Dereziński, Jan

AU - Gaß, Christian

AU - Ruba, Błażej

N1 - 39 pages

PY - 2023/4/12

Y1 - 2023/4/12

N2 - We compute bilinear integrals involving Macdonald and Gegenbauer functions. These integrals are convergent only for a limited range of parameters. However, when one uses generalized integrals they can be computed essentially without restricting the parameters. The generalized integral is a linear functional extending the standard integral to a certain class of functions involving finitely many homogeneous non-integrable terms at the edpoints of the interval. For generic values of parameters, generalized bilinear integrals of Macdonald and Gegenbauer functions can be obtained by analytic continuation from the region in which the integrals are convergent. In the case of integer parameters we obtain expressions with explicit additional terms related to an anomaly, namely the failure of the generalized integral to be scaling invariant.

AB - We compute bilinear integrals involving Macdonald and Gegenbauer functions. These integrals are convergent only for a limited range of parameters. However, when one uses generalized integrals they can be computed essentially without restricting the parameters. The generalized integral is a linear functional extending the standard integral to a certain class of functions involving finitely many homogeneous non-integrable terms at the edpoints of the interval. For generic values of parameters, generalized bilinear integrals of Macdonald and Gegenbauer functions can be obtained by analytic continuation from the region in which the integrals are convergent. In the case of integer parameters we obtain expressions with explicit additional terms related to an anomaly, namely the failure of the generalized integral to be scaling invariant.

KW - math.CA

KW - math-ph

KW - math.MP

KW - 33C05, 33C10, 47A52

M3 - Preprint

BT - Generalized integrals of Macdonald and Gegenbauer functions

PB - arXiv.org

ER -

ID: 382552940