A probabilistic proof of a formula for Jacobi polynomials by L. Carlitz
1968 ◽
Vol 64
(3)
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pp. 695-698
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Keyword(s):
Let be the Jacobi polynomial as defined by Szegö in (7) (see equation (4) below.) Carlitz in (2) presented among others the following formulaAlthough, as Carlitz claims, this formula may be derived directly from the definition of Jacobi polynomials, a probabilistic proof such as presented below may shed some new light on formula (1), as well as suggest probabilistic proofs for other similar formulas of Jacobi polynomials, e.g. those given by Manocha and Sharma in (4) and (5) and by Manocha in (3). In addition, it is quite possible that this method of proof will result in the derivation of some new formulas for Jacobi polynomials.
1953 ◽
Vol 5
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pp. 301-305
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Keyword(s):
1970 ◽
Vol 22
(3)
◽
pp. 582-593
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1968 ◽
Vol 16
(2)
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pp. 101-108
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Keyword(s):
1969 ◽
Vol 66
(1)
◽
pp. 105-107
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1971 ◽
Vol 70
(2)
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pp. 243-255
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1968 ◽
Vol 64
(3)
◽
pp. 687-690
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1985 ◽
Vol 37
(3)
◽
pp. 551-576
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1994 ◽
Vol 46
(06)
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pp. 1318-1337
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Keyword(s):
1967 ◽
Vol 63
(2)
◽
pp. 457-459
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1963 ◽
Vol 59
(2)
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pp. 363-371
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Keyword(s):