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Asymptotik bei Jacobi-Polynomen und Jacobi-Funktionen. (German) Zbl 0411.33008
33C45Orthogonal polynomials and functions of hypergeometric type
Full Text: DOI EuDML
[1] Askey, R.: Orthogonal Polynomials and Special Functions. Philadelphia: Society for Industrial and Applied Mathematics 1975 · Zbl 0298.33008
[2] Elliott, D.: Uniform Asymptotic Expansions of the Jacobi Polynomials and an Associated Function. Math. Comput.25, 309-314 (1971) · Zbl 0221.65027 · doi:10.1090/S0025-5718-1971-0294737-5
[3] Erdélyi, A., Magnus, W., Oberhettinger, F., Tricomi, F.G.: Higher Transcendental Functions. New York: McGraw-Hill (1953). Hier besonders Band 1, Kap. 2: ?The Hypergeometric Function? · Zbl 0052.29502
[4] Szegö, G.: Orthogonal Polynomials. 4. Auflage. Amer. Math. Soc. Colloquium Publications23. Providence, Rhode Island: American Mathematical Society 1975 · Zbl 0305.42011
[5] Szegö, G.: Asymptotische Entwicklungen der Jacobischen Polynome. Schr. Königsberger Gelehrtenges., naturw. Klasse10, 35-112 (1933-34) · Zbl 0007.20304
[6] Tricomi, F.G.: Vorlesungen über Orthogonalreihen. 2. Auflage. Berlin-Heidelberg-New York: Springer 1975
[7] Tricomi, F.G.: Expansion of the Hypergeometric Function in Series of Confluent ones and Application to the Jacobi Polynomials. Comment. Math. Helv.25, 196-204 (1951) · Zbl 0054.03302 · doi:10.1007/BF02566454
[8] Hahn, E.: Asymptotische Entwicklungen für Jacobi-Funktionen. Dissertation, Tübingen 1978