Question

How to prove that $ \ln{G(z+n)}+\ln{Γ(z+n)}=\ln{G(z)} +(n+1)\ln{Γ(z)}+\displaystyle \sum_{k=1}^{n} k\ln(z+n-k) $?

score 106 · Answer 1 · 2026-04-14 10:32:32

106

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How to prove that $ \ln{G(z+n)}+\ln{Γ(z+n)}=\ln{G(z)} +(n+1)\ln{Γ(z)}+\displaystyle \sum_{k=1}^{n} k\ln(z+n-k) $?

Published on 14 Apr 2026 - 10:32

score 459 · Answer 2 · 2026-04-08 17:57:29

459

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How to interpret a strange formula about $\zeta'(s)/\zeta(s)$

Published on 08 Apr 2026 - 17:57

score 127 · Answer 3 · 2026-04-16 14:07:51

127

Views

Show the function for which the Dirichlet generating series is $\zeta(2s)$ using only $\tau,\varphi,\sigma\text{ and }\mu$ or some explicit formula.

Published on 16 Apr 2026 - 14:07

score 59 · Answer 4 · 2026-04-15 04:15:01

59

Views

Why does $\sum\limits_{n=1}^\infty \frac{\nu(n)}{n^s} = \sum\limits_{m=1}^\infty \frac{1}{m^s}\sum\limits_p \frac{1}{p^s}$ hold

Published on 15 Apr 2026 - 4:15

score 141 · Answer 5 · 2026-04-09 18:31:20

141

Views

Positivity of partial Dirichlet series for a quadratic character?

Published on 09 Apr 2026 - 18:31

score 141 · Answer 6 · 2026-04-17 04:13:48

141

Views

Moments of derivatives of the Riemann zeta function

Published on 17 Apr 2026 - 4:13

score 137 · Answer 7 · 2026-04-16 12:47:00

137

Views

Elementary proof that $\lim_{n \to \infty} \prod_{i=1}^n (1-\frac{1}{p_i}) = 0$

Published on 16 Apr 2026 - 12:47

score 160 · Answer 8 · 2026-04-16 01:51:02

160

Views

How accurate is $\prod_{p < y} \left(1-\frac{1}{p}\right)$ for the number of $y$-rough integers?

Published on 16 Apr 2026 - 1:51

score 33 · Answer 9 · 2026-04-11 20:47:56

33

Views

Asymptotic behavior of a set of nonnegative integers whose sumset with itself is the nonnegative integers

Published on 11 Apr 2026 - 20:47

score 288 · Answer 10 · 2026-03-26 01:34:22

288

Views

Selberg Class- Ramanujan Conjecture

Published on 26 Mar 2026 - 1:34

score 73 · Answer 11 · 2026-04-14 18:38:23

73

Views

When is $li(x)$ a better estimate than $li(x) - (1/2) li(\sqrt{x})$?

Published on 14 Apr 2026 - 18:38

score 98 · Answer 12 · 2026-04-17 15:20:26

98

Views

$\sum_{m=1}^{N}\lfloor{\frac{N}{m}\rfloor} \sim N \log N$

Published on 17 Apr 2026 - 15:20

score 62 · Answer 13 · 2026-04-09 13:36:43

62

Views

A converge problem seems to related to Tauber theorem

Published on 09 Apr 2026 - 13:36

score 105 · Answer 14 · 2026-04-16 23:41:30

105

Views

The main term when counting $d(n)$ in arithmetic progressions

Published on 16 Apr 2026 - 23:41

score 70 · Answer 15 · 2026-04-15 03:06:53

70

Views

Can anyone please check/verify this proof?

Published on 15 Apr 2026 - 3:06

List Question

How to prove that $ \ln{G(z+n)}+\ln{Γ(z+n)}=\ln{G(z)} +(n+1)\ln{Γ(z)}+\displaystyle \sum_{k=1}^{n} k\ln(z+n-k) $?

How to interpret a strange formula about $\zeta'(s)/\zeta(s)$

Show the function for which the Dirichlet generating series is $\zeta(2s)$ using only $\tau,\varphi,\sigma\text{ and }\mu$ or some explicit formula.

Why does $\sum\limits_{n=1}^\infty \frac{\nu(n)}{n^s} = \sum\limits_{m=1}^\infty \frac{1}{m^s}\sum\limits_p \frac{1}{p^s}$ hold

Positivity of partial Dirichlet series for a quadratic character?

Moments of derivatives of the Riemann zeta function

Elementary proof that $\lim_{n \to \infty} \prod_{i=1}^n (1-\frac{1}{p_i}) = 0$

How accurate is $\prod_{p < y} \left(1-\frac{1}{p}\right)$ for the number of $y$-rough integers?

Asymptotic behavior of a set of nonnegative integers whose sumset with itself is the nonnegative integers

Selberg Class- Ramanujan Conjecture

When is $li(x)$ a better estimate than $li(x) - (1/2) li(\sqrt{x})$?

$\sum_{m=1}^{N}\lfloor{\frac{N}{m}\rfloor} \sim N \log N$

A converge problem seems to related to Tauber theorem

The main term when counting $d(n)$ in arithmetic progressions

Can anyone please check/verify this proof?

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