| 1. | This series expansion is extremely useful in solving partial differential equations.
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| 2. | This gives the following Taylor series expansion at x = 0.
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| 3. | Then one can compute the exponential function of that series expansion.
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| 4. | Furthermore, the series expansion of the gain is given by
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| 5. | This yields the infinite series expansion of the arctangent function.
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| 6. | The series expansion of the logarithm is then given by:
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| 7. | These are also the numbers appearing in the Taylor series expansion of and.
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| 8. | Using a Taylor's series expansion about c o yields the following:
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| 9. | :Do you know the MacLaurin series expansion for sin ( x )?
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| 10. | Also for essential singularities, residues often must be taken directly from series expansions.
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