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Examining the Mathematica algorithm for general Heun function calculation: a comparative analysis

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12 oct. 2024
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A. Ronveaux, Heuns Differential Equations. Oxford University Press, 1995. Search in Google Scholar

F. W. J. Olver, D. W. Lozier, R. F. Boisvert, and C. W. Clark, NIST Handbook of Mathematical Functions. Cambridge University Press, 2010. Search in Google Scholar

S. Y. Slavyanov and W. Lay, Special Functions. Oxford University Press, 2000. Search in Google Scholar

A. M. Ishkhanyan, Schrödinger potentials solvable in terms of the general heun functions, Annals of Physics, vol. 388, pp. 456–471, 2018. Search in Google Scholar

H. Grad and H. Rubin, Hydromagnetic equilibria and force free fields, J. Nucl. Energy, vol. 7, p. 284, 1958. Search in Google Scholar

V. D. Shafranov, Equilibrium of a plasma toroid in a magnetic field, Sov. Phys. JETP, vol. 37, p. 775, 1960. Search in Google Scholar

V. S. Mukhovatov and V. D. Shafranov, Plasma equilibrium in a tokamak, Nucl. Fusion, vol. 11, p. 605, 1971. Search in Google Scholar

A. Lupica, C. Cesarano, F. Crisanti, and A. Ishkhanian, Analytical solution of the three-dimensional laplace equation in terms of linear combinations of hypergeometric functions, Mathematics, vol. 9, p. 3316, 2021. Search in Google Scholar

F. Crisanti, C. Cesarano, and A. Ishkhanyan, Grad-shafranov equation in cap-cyclide coordinates: the heun function solution, Mathematics, vol. 11(9), p. 3316, 2023. Search in Google Scholar

A. M. Ishkhanyan, New solutions of heun’s general equation, J. Phys. A, vol. 36, p. L81, 2003. Search in Google Scholar

Maple Online Help, The five second order linear Heun equations and the corresponding Heun function solutions. Accessed on 30.03.2024. Search in Google Scholar

T. A. Ishkhanyan, From sine to Heun: 5 new functions for mathematics and physics in the Wolfram language. Accessed on 30.03.2024. Search in Google Scholar

Wolfram Research, HeunG, Wolfram language function. Search in Google Scholar

T. A. Ishkhanyan, T. A. Shahverdyan, and A. M. Ishkhanyan, Expansions of the solutions of the general heun equation governed by two-term recurrence relations for coefficients, Advances in High Energy Physics, vol. 2018, p. 4263678, 2018. Search in Google Scholar

A. M. Ishkhanian, Generalized hypergeometric solutions of the heun equation, Theor. Math. Phys., vol. 202, p. 1, 2020. Search in Google Scholar

L. J. Slater, Generalized Hypergeometric Functions. Cambridge University Press, 1966. Search in Google Scholar

R. S. Maier, The 192 solutions of the heun equation, Mathematics of Computation, vol. 76, pp. 811–843, 2007. Search in Google Scholar