formal series
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1: 16.11 Asymptotic Expansions
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§16.11(i) Formal Series
►For subsequent use we define two formal infinite series, and , as follows: ►
16.11.1
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16.11.2
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►The formal series (16.11.2) for converges if , and
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2: 10.70 Zeros
3: 3.10 Continued Fractions
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►Every convergent, asymptotic, or formal series
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►We say that it corresponds to the formal power series
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►We say that it is associated with the formal power series
in (3.10.7) if the expansion of its th convergent in ascending powers of , agrees with (3.10.7) up to and including the term in , .
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4: 1.17 Integral and Series Representations of the Dirac Delta
5: 1.8 Fourier Series
6: 16.5 Integral Representations and Integrals
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►In this event, the formal power-series expansion of the left-hand side (obtained from (16.2.1)) is the asymptotic expansion of the right-hand side as in the sector , where is an arbitrary small positive constant.
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7: 2.1 Definitions and Elementary Properties
8: Bibliography B
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Formal Power Series and Algebraic Combinatorics.
DIMACS Series in Discrete Mathematics and Theoretical Computer
Science, Vol. 24, American Mathematical Society, Providence, RI.
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9: 16.4 Argument Unity
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►Contiguous balanced series have parameters shifted by an integer but still balanced.
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►when the series on the right terminates and the series on the left converges.
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