Computations of general Heun functions from their integral series representations

T. Birkandan; P. L. Giscard; A. Tamar

doi:10.1109/DD52349.2021.9598600

Computations of general Heun functions from their integral series representations

T. Birkandan, P. L. Giscard, A. Tamar

Department of Physics Engineering

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

6 Citations (Scopus)

Abstract

We present a numerical implementation of the recently developed unconditionally convergent representation of general Heun functions as integral series. We produce two codes in Python available for download, one of which is especially aimed at reproducing the output of Mathematica's HeunG function. We show that the present code compares favorably with Mathematica's HeunG and with an Oc-tave/Matlab code of Motygin, in particular when the Heun function is to be evaluated at a large number of points if less accuracy is sufficient. We suggest further improvements concerning the accuracy and discuss the issue of singularities.

Original language	English
Title of host publication	Proceedings of the International Conference Days on Diffraction 2021, DD 2021
Editors	O.V. Motygin, A.P. Kiselev, L. I. Goray, A. S. Kirpichnikova
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	12-18
Number of pages	7
ISBN (Electronic)	9781665410892
DOIs	https://doi.org/10.1109/DD52349.2021.9598600
Publication status	Published - 2021
Event	2021 International Conference Days on Diffraction, DD 2021 - St. Petersburg, Russian Federation Duration: 31 May 2021 → 4 Jun 2021

Publication series

Name	Proceedings of the International Conference Days on Diffraction 2021, DD 2021

Conference

Conference	2021 International Conference Days on Diffraction, DD 2021
Country/Territory	Russian Federation
City	St. Petersburg
Period	31/05/21 → 4/06/21

Bibliographical note

Publisher Copyright:
© 2021 IEEE.

Funding

We thank the referee for constructive comments and suggestions. P.-L. G. is supported by the Agence Nationale de la Recherche young researcher grant № ANR-19-CE40-0006.

Funders	Funder number
Agence Nationale de la Recherche	ANR-19-CE40-0006

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10.1109/DD52349.2021.9598600

Cite this

Birkandan, T., Giscard, P. L., & Tamar, A. (2021). Computations of general Heun functions from their integral series representations. In O. V. Motygin, A. P. Kiselev, L. I. Goray, & A. S. Kirpichnikova (Eds.), Proceedings of the International Conference Days on Diffraction 2021, DD 2021 (pp. 12-18). (Proceedings of the International Conference Days on Diffraction 2021, DD 2021). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/DD52349.2021.9598600

Birkandan, T. ; Giscard, P. L. ; Tamar, A. / Computations of general Heun functions from their integral series representations. Proceedings of the International Conference Days on Diffraction 2021, DD 2021. editor / O.V. Motygin ; A.P. Kiselev ; L. I. Goray ; A. S. Kirpichnikova. Institute of Electrical and Electronics Engineers Inc., 2021. pp. 12-18 (Proceedings of the International Conference Days on Diffraction 2021, DD 2021).

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title = "Computations of general Heun functions from their integral series representations",

abstract = "We present a numerical implementation of the recently developed unconditionally convergent representation of general Heun functions as integral series. We produce two codes in Python available for download, one of which is especially aimed at reproducing the output of Mathematica's HeunG function. We show that the present code compares favorably with Mathematica's HeunG and with an Oc-tave/Matlab code of Motygin, in particular when the Heun function is to be evaluated at a large number of points if less accuracy is sufficient. We suggest further improvements concerning the accuracy and discuss the issue of singularities.",

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Birkandan, T, Giscard, PL & Tamar, A 2021, Computations of general Heun functions from their integral series representations. in OV Motygin, AP Kiselev, LI Goray & AS Kirpichnikova (eds), Proceedings of the International Conference Days on Diffraction 2021, DD 2021. Proceedings of the International Conference Days on Diffraction 2021, DD 2021, Institute of Electrical and Electronics Engineers Inc., pp. 12-18, 2021 International Conference Days on Diffraction, DD 2021, St. Petersburg, Russian Federation, 31/05/21. https://doi.org/10.1109/DD52349.2021.9598600

Computations of general Heun functions from their integral series representations. / Birkandan, T.; Giscard, P. L.; Tamar, A.
Proceedings of the International Conference Days on Diffraction 2021, DD 2021. ed. / O.V. Motygin; A.P. Kiselev; L. I. Goray; A. S. Kirpichnikova. Institute of Electrical and Electronics Engineers Inc., 2021. p. 12-18 (Proceedings of the International Conference Days on Diffraction 2021, DD 2021).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AB - We present a numerical implementation of the recently developed unconditionally convergent representation of general Heun functions as integral series. We produce two codes in Python available for download, one of which is especially aimed at reproducing the output of Mathematica's HeunG function. We show that the present code compares favorably with Mathematica's HeunG and with an Oc-tave/Matlab code of Motygin, in particular when the Heun function is to be evaluated at a large number of points if less accuracy is sufficient. We suggest further improvements concerning the accuracy and discuss the issue of singularities.

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BT - Proceedings of the International Conference Days on Diffraction 2021, DD 2021

A2 - Motygin, O.V.

A2 - Kiselev, A.P.

A2 - Goray, L. I.

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PB - Institute of Electrical and Electronics Engineers Inc.

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Birkandan T, Giscard PL, Tamar A. Computations of general Heun functions from their integral series representations. In Motygin OV, Kiselev AP, Goray LI, Kirpichnikova AS, editors, Proceedings of the International Conference Days on Diffraction 2021, DD 2021. Institute of Electrical and Electronics Engineers Inc. 2021. p. 12-18. (Proceedings of the International Conference Days on Diffraction 2021, DD 2021). doi: 10.1109/DD52349.2021.9598600

Computations of general Heun functions from their integral series representations

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Bibliographical note

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