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11: 10.57 Uniform Asymptotic Expansions for Large Order
12: 1.5 Calculus of Two or More Variables
2 f y x = y ( f x ) .
§1.5(iv) Leibniz’s Theorem for Differentiation of Integrals
1.5.24 d d x c d f ( x , y ) d y = c d f x d y , a < x < b .
13: 4.40 Integrals
14: 5.15 Polygamma Functions
Most properties of these functions follow straightforwardly by differentiation of properties of the psi function. …
15: 5.19 Mathematical Applications
16: 10.12 Generating Function and Associated Series
17: 1.9 Calculus of a Complex Variable
§1.9(ii) Continuity, Point Sets, and Differentiation
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: 5.17 Barnes’ G -Function (Double Gamma Function)
19: 4.26 Integrals
20: 7.7 Integral Representations