caa a22 4500 465825214 CHVBK 20180323112147.0 cr unu---uuuuu 170327e19901201xx s 000 0 eng 10.1007/BF02112283 doi (NATIONALLICENCE)springer-10.1007/BF02112283 Berg C. København's Univ., Matematisk Institut, Universitetsparken 5, DK-2100, Copenhagen Ø, Denmark aut Integrals involving Gegenbauer and Hermite polynomials on the imaginary axis [Elektronische Daten] [C. Berg] Summary: The integral ∫ -∞ ∞ [C 2n λ (it)]−2(1+t 2)−λ-1/2 dt is evaluated forλ > −1/2 whereC 2n λ is the Gegenbauer polynomial of degree 2n. Letting λ → ∞ gives the value ∫ -∞ ∞ [H 2n (it)]−2 e 1-1/2t 2 dt involving the Hermite polynomialH 2n of degree 2n. The result is obtained using Gegenbauer functions of the second kind. Birkhäuser Verlag, 1990 aequationes mathematicae Birkhäuser-Verlag 40/1(1990-12-01), 83-88 0001-9054 40:1<83 1990 40 10 https://doi.org/10.1007/BF02112283 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF02112283 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Berg C. København's Univ., Matematisk Institut, Universitetsparken 5, DK-2100, Copenhagen Ø, Denmark aut NATIONALLICENCE 773 0- aequationes mathematicae Birkhäuser-Verlag 40/1(1990-12-01), 83-88 0001-9054 40:1<83 1990 40 10 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer