An extension of typically-real functions and associated orthogonal polynomials
Iwona Naraniecka; Jan Szynal; Anna Tatarczak
Annales UMCS, Mathematica (2011)
- Volume: 65, Issue: 2, page 99-112
- ISSN: 2083-7402
Access Full Article
topAbstract
topHow to cite
topReferences
top- Chihara, T. S., An Introduction to Orthogonal Polynomials, Mathematics and its Applications. Vol. 13, Gordon and Breach Science Publishers, New York-London-Paris, 1978. Zbl0389.33008
- Goluzin, G. M., On typically real functions, Mat. Sbornik N.S. 27(69) (1950), 201-218 (Russian).
- Gasper, G., q-extensions of Clausen's formula and of the inequalities used by de Branges in his proof of the Bieberbach, Robertson and Milin conjectures, SIAM J. Math. Anal. 20 (1989), no. 4, 1019-1034. Zbl0679.33001
- Gasper, G., Rahman, M., Basic hypergeometric series, Encyclopedia of Mathematics and its Applications, 35. Cambridge University Press, Cambridge, 1990. Zbl0695.33001
- Kiepiela, K., Klimek, D., An extension of the Chebyshev polynomials, J. Comput. Appl. Math. 178 (2005), no. 1-2, 305-312. Zbl1068.33030
- Koczan, L., Szapiel, W., Sur certaines classes de fonctions holomorphes définies par une intègrale de Stieltjes, Ann. Univ. Mariae Curie-Skłodowska Sect. A 28 (1974), 39-51 (1976). Zbl0377.30014
- Koczan, L., Zaprawa, P., Domains of univalence for typically-real odd functions, Complex Var. Theory Appl. 48 (2003), no. 1, 1-17. Zbl1040.30004
- Mason, J. C., Handscomb, D. C., Chebyshev Polynomials, Chapman and Hall/ CRC, Boca Raton, FL, 2003.
- Robertson, M. S., On the coefficients of typically-real function, Bull. Amer. Math. Soc. 41 (1935), no. 8, 565-572. Zbl0012.21201
- Robertson, M. S., The sum of univalent functions, Duke Math. J. 37 (1970), 411-419. Zbl0201.40702
- Rogosinski, W., Über positive harmonische Entwicklungen und typisch-reelle Potenzreihen, Math. Z. 35 (1932), no. 1, 93-121. Zbl0003.39303