Jacobi Series for General Parameters via Hadamard Finite Part and Application to Nonhomogeneous Hypergeometric Equations
The representation of analytic functions as convergent series in Jacobi polynomials Pn(α,β) is reformulated using the Hadamard principal part of integrals for all α,β∈C∖{0,-1,-2,…}, α+β≠-2,-3,…. The coefficients of the series are given as usual integrals in the classical case (when Rα,Rβ>-1) or...
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| Format: | Article |
| Language: | English |
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Wiley
2019-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2019/2473212 |
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| author | Rodica D. Costin Marina David |
| author_facet | Rodica D. Costin Marina David |
| author_sort | Rodica D. Costin |
| collection | DOAJ |
| description | The representation of analytic functions as convergent series in Jacobi polynomials Pn(α,β) is reformulated using the Hadamard principal part of integrals for all α,β∈C∖{0,-1,-2,…}, α+β≠-2,-3,…. The coefficients of the series are given as usual integrals in the classical case (when Rα,Rβ>-1) or by their Hadamard principal part when they diverge. As an application it is shown that nonhomogeneous differential equations of hypergeometric type do generically have a unique solution which is analytic at both singular points in C. |
| format | Article |
| id | doaj-art-abdc0d44e3664abf8160818018eb76eb |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2019-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-abdc0d44e3664abf8160818018eb76eb2025-02-03T05:52:14ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252019-01-01201910.1155/2019/24732122473212Jacobi Series for General Parameters via Hadamard Finite Part and Application to Nonhomogeneous Hypergeometric EquationsRodica D. Costin0Marina David1Department of Mathematics, The Ohio State University, Columbus, OH 43210, USADepartment of Mathematics, The Ohio State University, Columbus, OH 43210, USAThe representation of analytic functions as convergent series in Jacobi polynomials Pn(α,β) is reformulated using the Hadamard principal part of integrals for all α,β∈C∖{0,-1,-2,…}, α+β≠-2,-3,…. The coefficients of the series are given as usual integrals in the classical case (when Rα,Rβ>-1) or by their Hadamard principal part when they diverge. As an application it is shown that nonhomogeneous differential equations of hypergeometric type do generically have a unique solution which is analytic at both singular points in C.http://dx.doi.org/10.1155/2019/2473212 |
| spellingShingle | Rodica D. Costin Marina David Jacobi Series for General Parameters via Hadamard Finite Part and Application to Nonhomogeneous Hypergeometric Equations International Journal of Mathematics and Mathematical Sciences |
| title | Jacobi Series for General Parameters via Hadamard Finite Part and Application to Nonhomogeneous Hypergeometric Equations |
| title_full | Jacobi Series for General Parameters via Hadamard Finite Part and Application to Nonhomogeneous Hypergeometric Equations |
| title_fullStr | Jacobi Series for General Parameters via Hadamard Finite Part and Application to Nonhomogeneous Hypergeometric Equations |
| title_full_unstemmed | Jacobi Series for General Parameters via Hadamard Finite Part and Application to Nonhomogeneous Hypergeometric Equations |
| title_short | Jacobi Series for General Parameters via Hadamard Finite Part and Application to Nonhomogeneous Hypergeometric Equations |
| title_sort | jacobi series for general parameters via hadamard finite part and application to nonhomogeneous hypergeometric equations |
| url | http://dx.doi.org/10.1155/2019/2473212 |
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