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Generating functions via Hankel and Stieltjes matrices. (English) Zbl 0961.15018
Summary: When the Hankel matrix formed from the sequence $$1,a_1,a_2, \dots$$ has an LDLT decomposition, we provide a constructive proof that the Stieltjes matrix $$S_L$$ associated with $$L$$ is tridiagonal. In the important case when $$L$$ is a Riordan matrix using ordinary or exponential generating functions, we determine the specific form that $$S_L$$ must have, and we demonstrate, constructively, a one-to-one correspondence between the generating function for the sequence and $$S_L$$. If $$L$$ is Riordan when using ordinary generating functions, we show how to derive a recurrence relation for the sequence.

##### MSC:
 15B57 Hermitian, skew-Hermitian, and related matrices 15A23 Factorization of matrices 05A15 Exact enumeration problems, generating functions
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