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If $f_n\to f$ uniformly on each ball, does it follow that $\left|\frac{f_n(tx)}{f_n(sx)}-\frac{f(tx)}{f(sx)}\right|\to0$ for all $s,t\in[0,1]$?

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#analysis #uniform-convergence
194
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Proof of De la Vallée-Poussin's Test

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#real-analysis #multivariable-calculus #convergence-divergence #solution-verification #uniform-convergence
59
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Show sequence of functions converges in metric space

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#real-analysis #uniform-convergence
87
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Uniform convergence of a sum of integral functions

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#real-analysis #sequences-and-series #functional-analysis #functions #uniform-convergence
48
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Does sequence converge in $C([0,1],\mathbb{R})$?

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#real-analysis #uniform-convergence
71
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Definition of uniform convergence

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#metric-spaces #definition #uniform-convergence
209
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Show the sequence converges uniformly

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#real-analysis #uniform-convergence
60
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Uniform convergence of an integral sequence of functions

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#real-analysis #sequences-and-series #functional-analysis #uniform-convergence
117
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Justifying: $\frac{\mathrm d}{\mathrm d c}{_2F_1}(a,b;c;x)=\sum_{k=1}^\infty\frac{\mathrm d}{\mathrm d c}\frac{(a)_k(b)_k}{(c)_k}\frac{z^k}{k!}$

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#real-analysis #sequences-and-series #uniform-convergence #hypergeometric-function
94
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Convergence of a series and its derivative

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#sequences-and-series #functional-analysis #normed-spaces #uniform-convergence
227
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Unsure how to proceed in showing that sin(x/n)n converges uniformly

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#real-analysis #uniform-convergence
177
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Uniform Convergence of series expansion of $\frac{\log(1+x)}{x}$

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#real-analysis #calculus #definite-integrals #uniform-convergence #riemann-zeta
454
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Uniform convergence of the inverse (solution verification)

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#real-analysis #continuity #solution-verification #uniform-convergence #inverse
54
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Applying Tannery's theorem to generalised hypergeometric functions

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#limits #uniform-convergence #hypergeometric-function
51
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Pointwise + Uniform Convergence:

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#limits #uniform-convergence #pointwise-convergence

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