feat(Analysis/SpecialFunctions/Gamma):add BinetKernel part 1

[jonwashburn]

PR 3a on HadamardFactorization pipeline
Co-authored with Matteo Cipollina (matteo.cipollina@yahoo.it)

---

[github-actions]

PR summary 18ef4ef4f3

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference
Mathlib.Analysis.SpecialFunctions.Gamma.Binet.Integral (new file)	1865

---

Declarations diff

+ K
+ K_eq_alt
+ K_eq_alt'
+ K_nonneg
+ K_pos
+ Ktilde
+ Ktilde_le
+ Ktilde_lt
+ Ktilde_nonneg
+ Ktilde_pos
+ Ktilde_zero
+ continuousOn_Ktilde_Ioi
+ differentiableOn_gAux
+ differentiableOn_gAux'
+ differentiableOn_gAux''
+ exp_mul_one_sub_lt_one
+ exp_sub_one_pos
+ f
+ f_at_one
+ f_deriv
+ f_deriv'
+ f_deriv_pos
+ f_nonneg
+ f_one_pos
+ f_zero
+ gAux
+ gAux'
+ gAux''
+ gAux'''
+ gAux'''_nonneg
+ gAux'''_pos
+ gAux''_nonneg
+ gAux''_pos
+ gAux''_zero
+ gAux'_nonneg
+ gAux'_pos
+ gAux'_zero
+ gAux_nonneg
+ gAux_pos
+ gAux_zero
+ hasDerivAt_gAux
+ hasDerivAt_gAux'
+ hasDerivAt_gAux''
+ monotoneOn_of_deriv_nonneg_Ici
+ nonneg_of_deriv_nonneg_Ici

You can run this locally as follows

## summary with just the declaration names:
./scripts/declarations_diff.sh <optional_commit>

## more verbose report:
./scripts/declarations_diff.sh long <optional_commit>

The doc-module for script/declarations_diff.sh contains some details about this script.

---

No changes to technical debt.

You can run this locally as

./scripts/technical-debt-metrics.sh pr_summary

• The relative value is the weighted sum of the differences with weight given by the inverse of the current value of the statistic.
• The absolute value is the relative value divided by the total sum of the inverses of the current values (i.e. the weighted average of the differences).

[github-actions]

🚨 PR Title Needs Formatting

Please update the title to match our commit style conventions.

Errors from script:

error: the PR title should be of the form
  abbrev: main title
or
  abbrev(scope): main title

Details on the required title format

The title should fit the following format:

<kind>(<optional-scope>): <subject>

<kind> is:

• feat (feature)
• fix (bug fix)
• doc (documentation)
• style (formatting, missing semicolons, ...)
• refactor
• test (when adding missing tests)
• chore (maintain)
• perf (performance improvement, optimization, ...)
• ci (changes to continuous integration, repo automation, ...)

<optional-scope> is a name of module or a directory which contains changed modules.
This is not necessary to include, but may be useful if the <subject> is insufficient.
The Mathlib directory prefix is always omitted.
For instance, it could be

• Data/Nat/Basic
• Algebra/Group/Defs
• Topology/Constructions

<subject> has the following constraints:

• do not capitalize the first letter
• no dot(.) at the end
• use imperative, present tense: "change" not "changed" nor "changes"

[metakunt]

Maybe other reviewers can help but isn't it possible for so many private lemmas to be in a private section? Usually for mathlib we expose all.

[metakunt]

Hey I see that you have 20 PR's opened in the span of a few hours, with one of those having at least 6k LoC. Maybe it makes sense to open a Zulip thread with your additions so that you get more direct feedback.

[or4nge19]

Hey I see that you have 20 PR's opened in the span of a few hours, with one of those having at least 6k LoC. Maybe it makes sense to open a Zulip thread with your additions so that you get more direct feedback.

Hi, these are prerequisites for the application of Hadamard Factorization to the zeta function. Some preliminary discussion anticipating the PR cycle here and here. Most of these are connected, the large one is on purpose still a draft as it will require to decide, among other things, whether to crate a dedicated folder for Hadamard/Divisor API.