| 1. | Repeated integration by parts will often lead to an asymptotic expansion.
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| 2. | There are always many different functions with any given asymptotic expansion.
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| 3. | Bernoulli numbers are also frequently used in other kinds of asymptotic expansions.
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| 4. | This function is related to the logarithm by the asymptotic expansion
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| 5. | This expansion follows directly from the asymptotic expansion for the exponential integral.
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| 6. | The horizontal axis is the number of terms in the asymptotic expansion.
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| 7. | A further application of this asymptotic expansion is for complex argument with constant.
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| 8. | And substituting by its not convergent asymptotic expansion.
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| 9. | The following example is the classical Poincar?type asymptotic expansion of the digamma function.
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| 10. | This results in an asymptotic expansion for.
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