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Is there some general technique to turn the operation of function into a continuous transformation from input to output?

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#real-analysis #calculus #complex-analysis #analytic-continuation
126
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How can the domains of all variables of this hyperoperation function be extended to the entire complex plane?

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#soft-question #recreational-mathematics #analytic-continuation #tetration #hyperoperation
39
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Convergence in a divergent double sum by substituting analytic continuation values

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#convergence-divergence #summation #divergent-series #analytic-continuation
15
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Solutions for $Re(z) > 2$ ,$f(z) = \sum_{1<i}^{\infty} f(i)^{\dfrac{z-i+1}{i}}$?

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#convergence-divergence #asymptotics #functional-equations #radicals #analytic-continuation
39
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Is this a valid analytic continuation of ζ(s) for 0 < Re(s) < 1?

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#complex-analysis #riemann-zeta #analytic-continuation
30
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Can we substitute values after analytic continuation

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#dirichlet-series #analytic-continuation
33
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Looking for a specific zeta function.

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#roots #residue-calculus #zeta-functions #analytic-continuation #meromorphic-functions
29
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Regularity of Cauchy-like integral

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#complex-analysis #cauchy-integral-formula #analytic-continuation
582
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Lipschitz functions (Theorem 1.4 of Condenser Capacities and Symmetrization in Geometric Function Theory)

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#complex-analysis #analysis #lipschitz-functions #plane-curves #analytic-continuation
82
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can we have a Taylor series expansion of the function $\frac{1}{\zeta(s)}$?

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#complex-analysis #power-series #zeta-functions #dirichlet-series #analytic-continuation
259
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Conditions to calculate an integral through a series expansion

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#real-analysis #integration #taylor-expansion #entire-functions #analytic-continuation
56
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Overlap in Implicit Function Theorem

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#complex-analysis #covering-spaces #implicit-function-theorem #analytic-continuation
16
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Dense subspace for arbitrary powers of a positive operator

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#functional-analysis #hilbert-spaces #analytic-continuation
130
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Analytic continuation for $\zeta(-x)$ vs $\frac{1}{(1-x)^2}$ at $x=1$

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#complex-analysis #riemann-zeta #analytic-continuation
32
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Analytic continuation of sums of Hypergeometric $_3F_2$ function pairs

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#fourier-transform #functional-equations #riemann-zeta #analytic-continuation #mellin-transform

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