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Link to original content: https://api.crossref.org/works/10.3390/AXIOMS8030102
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The Heun Project: Heun Functions, Their Generalizations and Applications. Available online: https:\/\/theheunproject.org\/bibliography.html."},{"key":"ref_2","first-page":"8621573","article-title":"Heun functions and some of their applications in physics","volume":"2018","year":"2018","journal-title":"Adv. High Energy Phys."},{"key":"ref_3","first-page":"121","article-title":"Zur Theorie der linearen Differentialgleichungen mit ver\u00e4nderlichen Coefficienten","volume":"66","author":"Fuchs","year":"1866","journal-title":"J. Reine Angew. Math."},{"key":"ref_4","first-page":"354","article-title":"Zur Theorie der linearen Differentialgleichungen mit ver\u00e4nderlichen Coefficienten. (Erg\u00e4nzungen zu der im 66sten Bande dieses Journals enthaltenen Abhandlung)","volume":"68","author":"Fuchs","year":"1868","journal-title":"J. Reine Angew. 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Generalized Hypergeometric Series, Stechert-Hafner Service Agency."},{"key":"ref_11","first-page":"624","article-title":"Generalized confluent hypergeometric solutions of the Heun confluent equation","volume":"338","author":"Ishkhanyan","year":"2018","journal-title":"Appl. Math. Comput."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Ishkhanyan, A.M. (2018). Generalized hypergeometric solutions of the Heun equation. arXiv.","DOI":"10.1155\/2018\/4263678"},{"key":"ref_13","first-page":"214","article-title":"Ueber die Integration der linearen Differentialgleichungen durch Reihen","volume":"76","author":"Frobenius","year":"1873","journal-title":"J. Reine Angew. Math."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"203","DOI":"10.1016\/0377-0427(93)E0246-I","article-title":"Co-recursive associated Jacobi polynomials","volume":"57","author":"Letessier","year":"1995","journal-title":"J. Comput. Appl. Math."},{"key":"ref_15","first-page":"371","article-title":"Some differential equations satisfied by hypergeometric functions","volume":"119","author":"Letessier","year":"1994","journal-title":"Intern. Ser. Numer. Math."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"139","DOI":"10.1090\/conm\/471\/09211","article-title":"P-symbols, Heun Identities, and 3F2 Identities","volume":"471","author":"Maier","year":"2008","journal-title":"Contemp. Math."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"4263678","DOI":"10.1155\/2018\/4263678","article-title":"Expansions of the solutions of the general Heun equation governed by two-term recurrence relations for coefficients","volume":"2018","author":"Ishkhanyan","year":"2018","journal-title":"Adv. High Energy Phys."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"085211","DOI":"10.1088\/1751-8113\/45\/8\/085211","article-title":"Heun\u2019s equation, generalized hypergeometric function and exceptional Jacobi polynomial","volume":"45","author":"Takemura","year":"2012","journal-title":"J. Phys. A"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"240","DOI":"10.1002\/sapm1942211240","article-title":"Linear differential equations with two-term recurrence formulas","volume":"21","year":"1942","journal-title":"J. Math. Phys."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"38","DOI":"10.1002\/sapm196443138","article-title":"An analysis of a second order linear ordinary differential equation with five regular singular points","volume":"43","author":"Crowson","year":"1964","journal-title":"J. Math. Phys."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"384","DOI":"10.1002\/sapm1965441384","article-title":"Hypergeometric solutions of a second-order linear ordinary differential equation with n-regular singular points","volume":"44","author":"Crowson","year":"1965","journal-title":"J. Math. Phys."},{"key":"ref_22","first-page":"96","article-title":"Finding 2F1 type solutions of differential equations with 5 singularities","volume":"46","author":"Kunwar","year":"2012","journal-title":"ACM Commun. Comput. Algebra"},{"key":"ref_23","unstructured":"Kunwar, V.J. (2014). Hypergeometric Solutions of Linear Differential Equations with Rational Function Coefficients. [Ph.D. Thesis, Florida State University]."},{"key":"ref_24","first-page":"23","article-title":"Solution of the linear differential equation of nth-order with four singular points","volume":"32","author":"Kruglov","year":"2010","journal-title":"Ann. Univ. Sci. Bp. Sect. Comp."},{"key":"ref_25","unstructured":"Ince, E.L. (1944). Ordinary Differential Equations, Dover."},{"key":"ref_26","unstructured":"Redkov, V.M., and Ovsiyuk, E.M. (2011). Quantum Mechanics in Spaces of Constant Curvature, Nova Science Publishers."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"155","DOI":"10.1007\/BF01181996","article-title":"Cesaro means in thermoelasticity of dipolar bodies","volume":"122","author":"Marin","year":"1997","journal-title":"Acta Mech."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"20002","DOI":"10.1209\/0295-5075\/115\/20002","article-title":"The third exactly solvable hypergeometric quantum-mechanical potential","volume":"115","author":"Ishkhanyan","year":"2016","journal-title":"EPL"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"456","DOI":"10.1016\/j.aop.2017.11.033","article-title":"Schr\u00f6dinger potentials solvable in terms of the general Heun functions","volume":"388","author":"Ishkhanyan","year":"2018","journal-title":"Ann. Phys."},{"key":"ref_30","unstructured":"Exton, H. (1976). Multiple Hypergeometric Functions and Applications, Halsted Press."},{"key":"ref_31","first-page":"143","article-title":"On a new family of Hermite polynomials associated to parabolic cylinder functions","volume":"141","author":"Dattoli","year":"2003","journal-title":"Appl. Math. Comput."},{"key":"ref_32","first-page":"1","article-title":"Generalized special functions in the description of fractional diffusive equations","volume":"10","author":"Cesarano","year":"2019","journal-title":"Commun. Appl. Ind. Math."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"445","DOI":"10.1007\/s00365-018-9424-8","article-title":"Appell hypergeometric expansions of the solutions of the general Heun equation","volume":"49","author":"Ishkhanyan","year":"2019","journal-title":"Constr. 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