Question

Fast approximation of $\sum_{i=1}^n e^{-\beta \ln(i)+\gamma{\ln}^2(i)}$ for large $n$

score 60 · Answer 1 · 2026-04-16 06:57:30

60

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Fast approximation of $\sum_{i=1}^n e^{-\beta \ln(i)+\gamma{\ln}^2(i)}$ for large $n$

Published on 16 Apr 2026 - 6:57

score 48 · Answer 2 · 2026-04-08 22:37:57

48

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Considering scaling factor in infinite approximations

Published on 08 Apr 2026 - 22:37

score 141 · Answer 3 · 2026-04-12 08:43:34

141

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What's the criterion for neglecting terms "much smaller than" other terms?

Published on 12 Apr 2026 - 8:43

score 24 · Answer 4 · 2026-04-17 15:48:16

24

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Approximate $\sum_{i=1}^n e^{-\beta \ln(i)+\gamma {\ln}^2(i)}$ for large $n$

Published on 17 Apr 2026 - 15:48

score 189 · Answer 5 · 2026-04-16 09:42:45

189

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How to prove $\sqrt {75025} + \sqrt {121393} + \sqrt {196418} + \sqrt{317811} \approx \sqrt {514229} + \sqrt {832040}$?

Published on 16 Apr 2026 - 9:42

score 238 · Answer 6 · 2026-04-14 05:48:11

238

Views

Why does interpolating a function on an interval using orthogonal polynomials give the best possible approximation in that interval?

Published on 14 Apr 2026 - 5:48

score 163 · Answer 7 · 2026-04-15 15:37:55

163

Views

Approximation for log of convex combination

Published on 15 Apr 2026 - 15:37

score 46 · Answer 8 · 2026-04-15 11:53:24

46

Views

How best to select $d$ from $[d_1, d_2]$ so $n/d$ is closest to $p/q$

Published on 15 Apr 2026 - 11:53

score 19 · Answer 9 · 2026-04-12 20:58:51

19

Views

Approximating polynomial under monotonicity constraint

Published on 12 Apr 2026 - 20:58

score 82 · Answer 10 · 2026-04-16 00:36:23

82

Views

$\int_0^{\infty} e^{-x}\cos xdx\approx \frac{h}{2}\frac{\sinh(h)}{\cosh(h)-\cos h} $

Published on 16 Apr 2026 - 0:36

score 311 · Answer 11 · 2026-03-25 11:09:35

311

Views

Simple functions dense in $C_{c}(X)$?

Published on 25 Mar 2026 - 11:09

score 84 · Answer 12 · 2026-04-12 05:15:32

84

Views

How well $\lfloor\sqrt{x}\rfloor + (x-\lfloor \sqrt{x}\rfloor^2)(2\lfloor \sqrt{x}\rfloor)^{-1}$ approximate $\sqrt{x}$?

Published on 12 Apr 2026 - 5:15

score 154 · Answer 13 · 2026-04-14 17:06:09

154

Views

Order of Magnitude of $\log{n!}$

Published on 14 Apr 2026 - 17:06

score 506 · Answer 14 · 2026-04-13 09:20:39

506

Views

Solving $x!=n$ without a calculator for large $n$

Published on 13 Apr 2026 - 9:20

score 34 · Answer 15 · 2026-04-14 04:05:39

34

Views

How did the following approximation arise in Bayati's paper on random graph generation

Published on 14 Apr 2026 - 4:05

List Question

Fast approximation of $\sum_{i=1}^n e^{-\beta \ln(i)+\gamma{\ln}^2(i)}$ for large $n$

Considering scaling factor in infinite approximations

What's the criterion for neglecting terms "much smaller than" other terms?

Approximate $\sum_{i=1}^n e^{-\beta \ln(i)+\gamma {\ln}^2(i)}$ for large $n$

How to prove $\sqrt {75025} + \sqrt {121393} + \sqrt {196418} + \sqrt{317811} \approx \sqrt {514229} + \sqrt {832040}$?

Why does interpolating a function on an interval using orthogonal polynomials give the best possible approximation in that interval?

Approximation for log of convex combination

How best to select $d$ from $[d_1, d_2]$ so $n/d$ is closest to $p/q$

Approximating polynomial under monotonicity constraint

$\int_0^{\infty} e^{-x}\cos xdx\approx \frac{h}{2}\frac{\sinh(h)}{\cosh(h)-\cos h} $

Simple functions dense in $C_{c}(X)$?

How well $\lfloor\sqrt{x}\rfloor + (x-\lfloor \sqrt{x}\rfloor^2)(2\lfloor \sqrt{x}\rfloor)^{-1}$ approximate $\sqrt{x}$?

Order of Magnitude of $\log{n!}$

Solving $x!=n$ without a calculator for large $n$

How did the following approximation arise in Bayati's paper on random graph generation

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