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15
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Find the the coefficient of $\,x^r\,$ in $\,(1+x+x^2)^n$

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#sequences-and-series #taylor-expansion #binomial-coefficients #multinomial-theorem
145
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Rigorous proof of Taylor expansion for matrix square root

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#linear-algebra #probability-theory #asymptotics #taylor-expansion
135
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Does the Taylor series of $\ln(x)$ about $1$ allow domain extension?

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#sequences-and-series #complex-analysis #complex-numbers #taylor-expansion #divergent-series
71
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Prove double inequality $2^{1-p}\le x^p+(1-x)^p \le1$

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#real-analysis #inequality #convex-analysis #taylor-expansion
65
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Is this the Taylor expansion of a known function?

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#complex-analysis #taylor-expansion
254
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What is the insight behind the usual proof of Taylor's Theorem?

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#real-analysis #taylor-expansion #proof-explanation
18
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How can I visualise $f(k,x)=\sum\limits_{n=0}^{\infty}\frac{x^{kn+1}}{(kn+1)!}(-1)^n$?

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#taylor-expansion
68
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Strange form of Taylor's Theorem for linearization

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#taylor-expansion
218
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Evaluate the sum using derivatives and generating functions

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#combinatorics #summation #power-series #taylor-expansion #generating-functions
66
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Prove the Taylor series for $f(x)=\sqrt{x+1}$ of $f$ about zero converges to $f$ for all $x$ in $(0,1)$.

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#limits #power-series #taylor-expansion
230
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Maclaurin Series by derivatives

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#calculus #taylor-expansion #binomial-coefficients
198
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noncompact difference

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#ordinary-differential-equations #derivatives #taylor-expansion #approximation #finite-differences
48
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Writing a MacLaurin expansion and finding the radius of convergence for the function: $f(x)= \ln(x+2)$

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#calculus #sequences-and-series #power-series #taylor-expansion
411
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Taylor's theorem and Lagrange remainders

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#real-analysis #analysis #derivatives #taylor-expansion
122
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The power series of $f(x)= \frac{1}{a-x}$

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#calculus #sequences-and-series #power-series #taylor-expansion

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