Question

Why does the approximation for exponents $(a+b)^c \approx a^{c-bc} (a+1)^{cb}$ work?

score 1.6k · Answer 1 · 2018-08-14 23:41:20

1.6k

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Why does the approximation for exponents $(a+b)^c \approx a^{c-bc} (a+1)^{cb}$ work?

Published on 14 Aug 2018 - 23:41

score 40 · Answer 2 · 2026-03-24 23:51:07

40

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Iterated backward difference quotient from splines

Published on 24 Mar 2026 - 23:51

score 1.1k · Answer 3 · 2018-08-17 04:35:43

1.1k

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Big O for Functions Approaching 0

Published on 17 Aug 2018 - 4:35

score 1.5k · Answer 4 · 2026-03-25 06:05:48

1.5k

Views

Order of convergence of midpoint rule

Published on 25 Mar 2026 - 6:05

score 172 · Answer 5 · 2018-08-20 17:23:55

172

Views

Tight upper bound for an improper integral

Published on 20 Aug 2018 - 17:23

score 132 · Answer 6 · 2026-03-25 16:21:19

132

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Asymptotic approximation of a sum involving log and binomial coefficient

Published on 25 Mar 2026 - 16:21

score 104 · Answer 7 · 2026-03-25 07:27:15

104

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Approximate Solution for $\int_{E_T}^\infty \frac{2 E b^\nu}{\Gamma (\nu)} \int_0^\infty x^{\nu -2}\exp(-b x)\exp(-(A^2 + E^2)/x) I_0(2EA/x) dx dE$

Published on 25 Mar 2026 - 7:27

score 220 · Answer 8 · 2026-03-24 06:20:11

220

Views

Intuition of error in Taylor appoximation and finding error in approximation of a function by a constant function

Published on 24 Mar 2026 - 6:20

score 53 · Answer 9 · 2018-08-26 10:18:40

53

Views

Patterns in error terms while approximating a function with its Taylor/McLauren expansion

Published on 26 Aug 2018 - 10:18

score 319 · Answer 10 · 2018-08-26 12:19:57

319

Views

Convergent piecewise-constant approximation of l.s.c function

Published on 26 Aug 2018 - 12:19

score 133 · Answer 11 · 2018-08-28 12:46:01

133

Views

Asymptotic approximation of the expression $\sum _{i=0}^n \log (\binom{n}{i}+1)$

Published on 28 Aug 2018 - 12:46

score 251 · Answer 12 · 2018-08-28 19:23:25

251

Views

Large $x$ expansion of $\ln \frac{1+e^{ax}}{1+e^{-bx}}$

Published on 28 Aug 2018 - 19:23

score 962 · Answer 13 · 2026-03-25 02:40:41

962

Views

How to linearize the distance formula?

Published on 25 Mar 2026 - 2:40

score 275 · Answer 14 · 2026-03-25 03:07:40

275

Views

Constant term in Stirling type formula for $\sum^N_{n=1} H_n \cdot \ln(n)$

Published on 25 Mar 2026 - 3:07

score 121 · Answer 15 · 2018-08-29 16:22:14

121

Views

Asymptotic approximation of the expression $\sum^{N}_{i=0}\log\Bigg[\binom{\binom{N+1}{i}}{t_i}\Bigg]$

Published on 29 Aug 2018 - 16:22

List Question

Why does the approximation for exponents $(a+b)^c \approx a^{c-bc} (a+1)^{cb}$ work?

Iterated backward difference quotient from splines

Big O for Functions Approaching 0

Order of convergence of midpoint rule

Tight upper bound for an improper integral

Asymptotic approximation of a sum involving log and binomial coefficient

Approximate Solution for $\int_{E_T}^\infty \frac{2 E b^\nu}{\Gamma (\nu)} \int_0^\infty x^{\nu -2}\exp(-b x)\exp(-(A^2 + E^2)/x) I_0(2EA/x) dx dE$

Intuition of error in Taylor appoximation and finding error in approximation of a function by a constant function

Patterns in error terms while approximating a function with its Taylor/McLauren expansion

Convergent piecewise-constant approximation of l.s.c function

Asymptotic approximation of the expression $\sum _{i=0}^n \log (\binom{n}{i}+1)$

Large $x$ expansion of $\ln \frac{1+e^{ax}}{1+e^{-bx}}$

How to linearize the distance formula?

Constant term in Stirling type formula for $\sum^N_{n=1} H_n \cdot \ln(n)$

Asymptotic approximation of the expression $\sum^{N}_{i=0}\log\Bigg[\binom{\binom{N+1}{i}}{t_i}\Bigg]$

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