Question

Is it possible to generalize Ramanujan's lower bound for factorials when $\{\frac{x}{b_2}\} + \{\frac{x}{b_3}\} \ge 1$?

score 75 · Answer 1 · 2026-04-06 03:13:11

75

Views

Is it possible to generalize Ramanujan's lower bound for factorials when $\{\frac{x}{b_2}\} + \{\frac{x}{b_3}\} \ge 1$?

Published on 06 Apr 2026 - 3:13

score 93 · Answer 2 · 2026-04-06 03:13:12

93

Views

Is it possible to generalize Ramanujan's lower bound for factorials when $\{\frac{x}{b_2}\} + \{\frac{x}{b_3}\} < 1$?

Published on 06 Apr 2026 - 3:13

score 177 · Answer 3 · 2013-04-15 02:10:42

177

Views

How to compare two ratios of gamma functions?

Published on 15 Apr 2013 - 2:10

score 379 · Answer 4 · 2013-04-15 04:53:54

379

Views

Looking for help understanding the asymptotic expansion of the digamma function

Published on 15 Apr 2013 - 4:53

score 200 · Answer 5 · 2026-04-06 03:08:16

200

Views

Proving that a specific gamma function is a guaranteed lower bound for a factorial function

Published on 06 Apr 2026 - 3:08

score 489 · Answer 6 · 2013-04-18 01:18:22

489

Views

Prove an identity involving Gamma function and Gaussian hypergeometric function

Published on 18 Apr 2013 - 1:18

score 102 · Answer 7 · 2013-04-25 15:49:34

102

Views

Gamma Function Problem

Published on 25 Apr 2013 - 15:49

score 82 · Answer 8 · 2013-04-26 22:57:17

82

Views

Gamma functions and their arguments

Published on 26 Apr 2013 - 22:57

score 138 · Answer 9 · 2026-03-25 13:49:32

138

Views

Looking for help in understanding Jitsuro Nagura's analysis of the upper bound for $\psi(x)$

Published on 25 Mar 2026 - 13:49

score 49 · Answer 10 · 2013-05-03 04:40:45

49

Views

What's the most straight forward way to show that a function is increasing?

Published on 03 May 2013 - 4:40

score 107 · Answer 11 · 2026-04-06 04:38:33

107

Views

Trying to generalize an inequality from Jitsuro Nagura: Does this work?

Published on 06 Apr 2026 - 4:38

score 98 · Answer 12 · 2026-04-06 04:36:14

98

Views

Do these inequalities regarding the gamma function and factorials work?

Published on 06 Apr 2026 - 4:36

score 163 · Answer 13 · 2026-04-06 04:39:57

163

Views

Using Stirling's Formula to approximate a difference of logarithms of factorials in the same way as Jitsuro Nagura.

Published on 06 Apr 2026 - 4:39

score 184 · Answer 14 · 2026-03-25 13:46:46

184

Views

Generalizing Jitsuro Nagura's result: my resulting upper bound for the second chebyshev function is too low. What am I doing wrong?

Published on 25 Mar 2026 - 13:46

score 1k · Answer 15 · 2013-05-08 01:49:37

1k

Views

Closed form for $\sum_{n=1}^\infty\frac{(-1)^n n^4 H_n}{2^n}$

Published on 08 May 2013 - 1:49

List Question

Is it possible to generalize Ramanujan's lower bound for factorials when $\{\frac{x}{b_2}\} + \{\frac{x}{b_3}\} \ge 1$?

Is it possible to generalize Ramanujan's lower bound for factorials when $\{\frac{x}{b_2}\} + \{\frac{x}{b_3}\} < 1$?

How to compare two ratios of gamma functions?

Looking for help understanding the asymptotic expansion of the digamma function

Proving that a specific gamma function is a guaranteed lower bound for a factorial function

Prove an identity involving Gamma function and Gaussian hypergeometric function

Gamma Function Problem

Gamma functions and their arguments

Looking for help in understanding Jitsuro Nagura's analysis of the upper bound for $\psi(x)$

What's the most straight forward way to show that a function is increasing?

Trying to generalize an inequality from Jitsuro Nagura: Does this work?

Do these inequalities regarding the gamma function and factorials work?

Using Stirling's Formula to approximate a difference of logarithms of factorials in the same way as Jitsuro Nagura.

Generalizing Jitsuro Nagura's result: my resulting upper bound for the second chebyshev function is too low. What am I doing wrong?

Closed form for $\sum_{n=1}^\infty\frac{(-1)^n n^4 H_n}{2^n}$

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