- Research Article
- Open Access
© Hongshun Ruan. 2009
- Received: 25 August 2008
- Accepted: 3 January 2009
- Published: 14 January 2009
- Real Number
- Root System
- Special Function
- Number Theory
- Orthogonal Polynomial
provided that the series converges.
In order to prove the main result, we need to introduce two lemmas.
(1.9) is proved.
Thus, (1.13) follows. We complete the proof.
From (2.4) and (1.6), (2.1) holds. The proof is completed.
As the application of Theorem 2.1, in this section, we obtain some results. First, we give following lemma.
From (3.2), (3.1) holds.
Combining (3.4)–(3.7), (3.3) holds.
which by combining with (3.10), implies (3.9).
Combining (3.15) and (3.16), (3.14) follows.
From (3.23) and (1.5), (3.17) follows.
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