differentiation

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11: 23.14 Integrals

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12: Philip J. Davis

… ►Davis also co-authored a second Chapter, “Numerical Interpolation, Differentiation, and Integration” with Ivan Polonsky. …

13: 1.8 Fourier Series

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§1.8(iii) Integration and Differentiation

… ►If a function $f(x)\in C^2[0,2\pi ]$ is periodic, with period $2\pi$, then the series obtained by differentiating the Fourier series for $f(x)$ term by term converges at every point to $f^{\prime }(x)$. …

14: 4.40 Integrals

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15: 10.12 Generating Function and Associated Series

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16: 18.40 Methods of Computation

… ►See Gautschi (1983) for examples of numerically stable and unstable use of the above recursion relations, and how one can then usefully differentiate between numerical results of low and high precision, as produced thereby. … ►Interpolation of the midpoints of the jumps followed by differentiation with respect to $x$ yields a Stieltjes–Perron inversion to obtain $w^{\mathrm{RCP}}(x)$ to a precision of $\sim 4$ decimal digits for $N=120$. … ►Here $x(t,N)$ is an interpolation of the abscissas $x_{i,N},i=1,2,\mathrm{\dots },N$, that is, $x(i,N)=x_{i,N}$, allowing differentiation by $i$. …

17: 1.9 Calculus of a Complex Variable

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§1.9(ii) Continuity, Point Sets, and Differentiation

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Differentiation

… ►Differentiability automatically implies continuity. ►

Cauchy–Riemann Equations

… ►Lastly, a power series can be differentiated any number of times within its circle of convergence: …

18: 5.15 Polygamma Functions

… ►Most properties of these functions follow straightforwardly by differentiation of properties of the psi function. …

19: 5.17 Barnes’ $G$-Function (Double Gamma Function)

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20: 4.26 Integrals

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