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

Fizik Mühendisliği Bölümü

Araştırma sonucu: Kitap/Rapor/Konferans Bildirisinde Bölüm › Konferans katkısı › bilirkişi

6 Atıf (Scopus)

Özet

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.

Orijinal dil	İngilizce
Ana bilgisayar yayını başlığı	Proceedings of the International Conference Days on Diffraction 2021, DD 2021
Editörler	O.V. Motygin, A.P. Kiselev, L. I. Goray, A. S. Kirpichnikova
Yayınlayan	Institute of Electrical and Electronics Engineers Inc.
Sayfalar	12-18
Sayfa sayısı	7
ISBN (Elektronik)	9781665410892
DOI'lar	https://doi.org/10.1109/DD52349.2021.9598600
Yayın durumu	Yayınlandı - 2021
Etkinlik	2021 International Conference Days on Diffraction, DD 2021 - St. Petersburg, Russian Federation Süre: 31 May 2021 → 4 Haz 2021

Yayın serisi

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

???event.eventtypes.event.conference???

???event.eventtypes.event.conference???	2021 International Conference Days on Diffraction, DD 2021
Ülke/Bölge	Russian Federation
Şehir	St. Petersburg
Periyot	31/05/21 → 4/06/21

Bibliyografik not

Publisher Copyright:
© 2021 IEEE.

Finansman

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.

Finansörler	Finansör numarası
Agence Nationale de la Recherche	ANR-19-CE40-0006

Belgeye Erişim

10.1109/DD52349.2021.9598600

Diğer Dosyalar ve Linkler

Link to publication in Scopus

Alıntı Yap

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. editör / 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.",

author = "T. Birkandan and Giscard, {P. L.} and A. Tamar",

note = "Publisher Copyright: {\textcopyright} 2021 IEEE.; 2021 International Conference Days on Diffraction, DD 2021 ; Conference date: 31-05-2021 Through 04-06-2021",

year = "2021",

doi = "10.1109/DD52349.2021.9598600",

language = "English",

series = "Proceedings of the International Conference Days on Diffraction 2021, DD 2021",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

pages = "12--18",

editor = "O.V. Motygin and A.P. Kiselev and Goray, {L. I.} and Kirpichnikova, {A. S.}",

booktitle = "Proceedings of the International Conference Days on Diffraction 2021, DD 2021",

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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).

Araştırma sonucu: Kitap/Rapor/Konferans Bildirisinde Bölüm › Konferans katkısı › bilirkişi

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AU - Birkandan, T.

AU - Giscard, P. L.

AU - Tamar, A.

PY - 2021

Y1 - 2021

N2 - 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.

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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U2 - 10.1109/DD52349.2021.9598600

DO - 10.1109/DD52349.2021.9598600

M3 - Conference contribution

AN - SCOPUS:85123289977

T3 - Proceedings of the International Conference Days on Diffraction 2021, DD 2021

SP - 12

EP - 18

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

A2 - Motygin, O.V.

A2 - Kiselev, A.P.

A2 - Goray, L. I.

A2 - Kirpichnikova, A. S.

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 2021 International Conference Days on Diffraction, DD 2021

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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, editörler, 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

Özet

Yayın serisi

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Bibliyografik not

Finansman

Belgeye Erişim

Diğer Dosyalar ve Linkler

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