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Truncations of Gauss' square exponent theorem

Ji-Cai Liu, Shan-Shan Zhao (2022)

Czechoslovak Mathematical Journal

We establish two truncations of Gauss’ square exponent theorem and a finite extension of Euler’s identity. For instance, we prove that for any positive integer n , k = 0 n ( - 1 ) k 2 n - k k ( q ; q 2 ) n - k q k + 1 2 = k = - n n ( - 1 ) k q k 2 , where n m = k = 1 m 1 - q n - k + 1 1 - q k and ( a ; q ) n = k = 0 n - 1 ( 1 - a q k ) .

Two limit transitions involving multivariable BC type Askey-Wilson polynomials

Jasper Stokman (1997)

Banach Center Publications

In the first part (without proofs) an orthogonality measure with partly discrete and partly continuous support will be introduced for the five parameter family of multivariable BC type Askey-Wilson polynomials. In the second part, the limit transitions from BC type Askey-Wilson polynomials to BC type big and little q-Jacobi polynomials will be described in detail.

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