differentiation
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1: 27.20 Methods of Computation: Other Number-Theoretic Functions
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►A recursion formula obtained by differentiating (27.14.18) can be used to calculate Ramanujan’s function , and the values can be checked by the congruence (27.14.20).
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2: 3.4 Differentiation
§3.4 Differentiation
… ►and follows from the differentiated form of (3.3.4). … ► ►§3.4(ii) Analytic Functions
… ►3: 2.1 Definitions and Elementary Properties
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§2.1(ii) Integration and Differentiation
… ►Differentiation requires extra conditions. …This result also holds with both ’s replaced by ’s. … ►means that for each , the difference between and the th partial sum on the right-hand side is as in . … ►Differentiation, however, requires the kind of extra conditions needed for the symbol (§2.1(ii)). …4: 7.10 Derivatives
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5: 1.8 Fourier Series
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§1.8(iii) Integration and Differentiation
… ►If a function is periodic, with period , then the series obtained by differentiating the Fourier series for term by term converges at every point to . …6: 4.10 Integrals
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7: 9.10 Integrals
8: 10.57 Uniform Asymptotic Expansions for Large Order
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9: 23.14 Integrals
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10: Philip J. Davis
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►Davis also co-authored a second Chapter, “Numerical Interpolation, Differentiation, and Integration” with Ivan Polonsky.
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