Question

Leading order asymptotic behaviour of the integral $\int^1_0 \cos(xt^3)\tan(t)dt$

score 414 · Answer 1 · 2026-03-25 14:24:41

414

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Leading order asymptotic behaviour of the integral $\int^1_0 \cos(xt^3)\tan(t)dt$

Published on 25 Mar 2026 - 14:24

score 181 · Answer 2 · 2026-04-13 19:55:50

181

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A problem from Applied Asymptotic Analysis by Peter D. Miller (Exercise 1.8)

Published on 13 Apr 2026 - 19:55

score 49 · Answer 3 · 2026-04-20 14:07:33

49

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Does a connection exist between the roots of $\mathrm{Si}\left(\frac{z}{2}\right)$ and the roots of its derivative?

Published on 20 Apr 2026 - 14:07

score 96 · Answer 4 · 2026-04-15 10:10:27

96

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Proof verification: if $a_n=\Omega(C^n)$ as $n\to\infty$ for every $C>1$, then $a_n=\omega(C^n)$ as $n\to\infty$.

Published on 15 Apr 2026 - 10:10

score 32 · Answer 5 · 2026-04-12 05:18:36

32

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If Mellin transform of a function has a pole at $s=\sigma+it$, then the function is not $o(x^{\sigma})$

Published on 12 Apr 2026 - 5:18

score 193 · Answer 6 · 2026-04-11 04:29:15

193

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Approximating Harmonic numbers $H_n$ with degree 3 polynomial and $\ln$.

Published on 11 Apr 2026 - 4:29

score 223 · Answer 7 · 2026-04-10 13:40:12

223

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How to Integrate the Gamma Function

Published on 10 Apr 2026 - 13:40

score 187 · Answer 8 · 2026-04-17 23:58:42

187

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$\lim_{n\to\infty} \left(\frac{e}{n}\right)^n \int_0^n |x(x-1)(x-2)\dots(x-n)|dx$

Published on 17 Apr 2026 - 23:58

score 51 · Answer 9 · 2026-04-15 04:43:22

51

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The implications of: $\sum ^\infty _{k=1} \frac{a_k}{n^k}=O(\frac 1 n)$

Published on 15 Apr 2026 - 4:43

score 50 · Answer 10 · 2026-04-10 12:19:42

50

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Determining the asymptotic relationship between two logarithmic functions.

Published on 10 Apr 2026 - 12:19

score 154 · Answer 11 · 2026-04-09 10:04:32

154

Views

Asymptotic expressions for the coordinates of the turning point in $x\in(0,1)$ on $y=|x(x-1)(x-2)\dots(x-n)|$ as $n\to\infty$?

Published on 09 Apr 2026 - 10:04

score 80 · Answer 12 · 2026-04-15 18:32:40

80

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How is the integral form of the Bessel function related to infinite sum form that results by directly solving the differential equation?

Published on 15 Apr 2026 - 18:32

score 95 · Answer 13 · 2026-04-13 08:06:27

95

Views

Asymptotics of incomplete gamma function

Published on 13 Apr 2026 - 8:06

score 45 · Answer 14 · 2026-04-15 15:04:53

45

Views

Finding Polynomials of Lowest Degree that is similar to $f$ as $x\to a$

Published on 15 Apr 2026 - 15:04

score 115 · Answer 15 · 2026-04-16 07:37:08

115

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Find the limit $\displaystyle{\lim_{x\to 0}\frac{\sin(x)\sin^{-1}(x)-\sinh(x)\sinh^{-1}(x)}{x^2(\cos(x)-\cosh(x)+\sec(x)-\text{sech}(x))}}$

Published on 16 Apr 2026 - 7:37

List Question

Leading order asymptotic behaviour of the integral $\int^1_0 \cos(xt^3)\tan(t)dt$

A problem from Applied Asymptotic Analysis by Peter D. Miller (Exercise 1.8)

Does a connection exist between the roots of $\mathrm{Si}\left(\frac{z}{2}\right)$ and the roots of its derivative?

Proof verification: if $a_n=\Omega(C^n)$ as $n\to\infty$ for every $C>1$, then $a_n=\omega(C^n)$ as $n\to\infty$.

If Mellin transform of a function has a pole at $s=\sigma+it$, then the function is not $o(x^{\sigma})$

Approximating Harmonic numbers $H_n$ with degree 3 polynomial and $\ln$.

How to Integrate the Gamma Function

$\lim_{n\to\infty} \left(\frac{e}{n}\right)^n \int_0^n |x(x-1)(x-2)\dots(x-n)|dx$

The implications of: $\sum ^\infty _{k=1} \frac{a_k}{n^k}=O(\frac 1 n)$

Determining the asymptotic relationship between two logarithmic functions.

Asymptotic expressions for the coordinates of the turning point in $x\in(0,1)$ on $y=|x(x-1)(x-2)\dots(x-n)|$ as $n\to\infty$?

How is the integral form of the Bessel function related to infinite sum form that results by directly solving the differential equation?

Asymptotics of incomplete gamma function

Finding Polynomials of Lowest Degree that is similar to $f$ as $x\to a$

Find the limit $\displaystyle{\lim_{x\to 0}\frac{\sin(x)\sin^{-1}(x)-\sinh(x)\sinh^{-1}(x)}{x^2(\cos(x)-\cosh(x)+\sec(x)-\text{sech}(x))}}$

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