Computations of general Heun functions from their integral series representations


Creative Commons License

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

Days on Diffraction 2021, Sankt-Peterburg, Rusya, 31 Mayıs - 04 Haziran 2021, ss.12-18

  • Yayın Türü: Bildiri / Tam Metin Bildiri
  • Doi Numarası: 10.1109/dd52349.2021.9598600
  • Basıldığı Şehir: Sankt-Peterburg
  • Basıldığı Ülke: Rusya
  • Sayfa Sayıları: ss.12-18
  • İstanbul Teknik Üniversitesi Adresli: Evet

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 Octave/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.