Integrals involving Gegenbauer and Hermite polynomials on the imaginary axis |
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Authors: | C Berg |
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Institution: | (1) København's Univ., Matematisk Institut, Universitetsparken 5, DK-2100 Copenhagen Ø, Denmark |
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Abstract: | Summary The integral
-
C
2n
(it)]–2(1+t
2)–-1/2
dt is evaluated for > –1/2 whereC
2n
is the Gegenbauer polynomial of degree 2n. Letting 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. |
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Keywords: | Primary 33A65 Secondary 33A50 |
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