[Merged by Bors] - refactor(Analysis): golf Mathlib/Analysis/SpecialFunctions/Gamma/Basic

[yuanyi-350]

• rewrites Gamma_eq_integral using Complex.GammaIntegral_ofReal instead of an inline set-integral congruence

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Extracted from #37968, migrated from #38076.

[github-actions]

PR summary c3e588b468

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference

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Declarations diff

No declarations were harmed in the making of this PR! 🐙

You can run this locally as follows

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

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

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

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Decrease in tech debt: (relative, absolute) = (1.00, 0.00)

Current number	Change	Type
6533	-1	backward.isDefEq.respectTransparency

Current commit 5c09b5fa98
Reference commit c3e588b468

You can run this locally as

./scripts/reporting/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).

[yuanyi-350]

I ran a profiler comparison for the changed declarations in this PR.

Results (seconds):

• Real.Gamma_eq_integral: 0.271334 -> 0.024531 (-91.0%)

Overall:

• Both changed declarations are faster.

[themathqueen]

Thanks!

maintainer merge

[github-actions]

🚀 Pull request has been placed on the maintainer queue by themathqueen.

[bryangingechen]

Thanks!
bors r+

[mathlib-bors]

Pull request successfully merged into master.

Build succeeded:

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