Transformation of certain bilinear generating functions

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Erdélyi's generalizations of the Hardy-Hille formula are extended to series involving arbitrary coefficients; see(1.6), …,(1.9) below. These identities may be thought of as identities in formal power series. The proofs are simple: each identity in shown to be equivalent to an algebraic identity that is easily verified.


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Supported in part by NSF grant GP-7855.

Entrata in Redazione il 18 novembre 1969.

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Carlitz, L. Transformation of certain bilinear generating functions. Annali di Matematica 86, 155–168 (1970).

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  • Generate Function
  • Power Series
  • Formal Power Series
  • Algebraic Identity
  • Arbitrary Coefficient