feat(Analysis/SpecialFunctions): generating function of besselJ

[wwylele]

This proves $e^{\frac{1}{2}z(t-t^{-1})}=\sum_{m=-\infty}^{\infty}t^{m}J_{m}\left(z\right)$

---

• depends on: feat(Analysis/SpecialFunctions): derivative of Bessel function of the first kind #42825
• depends on: feat(Analysis/Normed): norm and Multiset.prod commute #43979

[github-actions]

PR summary dd9dfb87f3

Import changes for modified files

Dependency changes

File	Base Count	Head Count	Change
Mathlib.Analysis.SpecialFunctions.Bessel	2782	2797	+15 (+0.54%)
Mathlib.Analysis.SpecialFunctions.RegularizedHypergeometric	2780	2781	+1 (+0.04%)

Import changes for all files

Files	Import difference
Mathlib.Analysis.SpecialFunctions.RegularizedHypergeometric	1
Mathlib.Analysis.SpecialFunctions.Bessel	15

---

Declarations diff (regex)

+ Multiset.nnnorm_prod_map
+ Multiset.norm_prod_map
+ analyticOnNhd_tsum_besselJ_mul_pow
+ deriv_besselJ_mul_pow_le
+ deriv_regularizedHGFun
+ hasSum_besselJ_mul_pow
+ mul_deriv_besselJ_eq_besselJ_add_one
+ mul_deriv_besselJ_eq_besselJ_add_one_int
+ mul_deriv_besselJ_eq_besselJ_sub_one
+ mul_deriv_besselJ_eq_besselJ_sub_one_int
+ mul_regularizedHGFunCoeff
+ mul_regularizedHGFunCoeff_of_mem_right
+ norm_Gamma_le_norm_Gamma_add_of_one_le_re
+ norm_Gamma_le_norm_Gamma_add_one
+ norm_besselJ_le_exp
+ norm_besselJ_le_exp_int
+ regularizedHGFun_le_exp_of_one_le_re
+ regularizedHGFun_zero_singleton_eq_mul_add_mul
+ regularizedHGFun_zero_singleton_eq_mul_add_mul_aux
+ summable_aux
+ summable_besselJ_mul_pow
+ summable_deriv_HGF
+ tsum_besselJ_mul_pow
+ two_mul_deriv_besselJ
+ two_mul_deriv_besselJ_int
+ two_mul_self_mul_besselJ

You can run this locally as follows

## from your `mathlib4` directory:
git clone https://github.com/leanprover-community/mathlib-ci.git ../mathlib-ci

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

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

The doc-module for scripts/pr_summary/declarations_diff.sh in the mathlib-ci repository contains some details about this script.

Declarations diff (Lean)

✅ Lean-aware diff — post-build, computed from the Lean environment (commit dd9dfb8).

• +24 new declarations
• −0 removed declarations

+Complex.analyticOnNhd_tsum_besselJ_mul_pow
+Complex.deriv_regularizedHGFun
+Complex.hasSum_besselJ_mul_pow
+Complex.mul_deriv_besselJ_eq_besselJ_add_one
+Complex.mul_deriv_besselJ_eq_besselJ_add_one_int
+Complex.mul_deriv_besselJ_eq_besselJ_sub_one
+Complex.mul_deriv_besselJ_eq_besselJ_sub_one_int
+Complex.mul_regularizedHGFunCoeff
+Complex.mul_regularizedHGFunCoeff_of_mem_right
+Complex.norm_Gamma_le_norm_Gamma_add_of_one_le_re
+Complex.norm_Gamma_le_norm_Gamma_add_one
+Complex.norm_besselJ_le_exp
+Complex.norm_besselJ_le_exp_int
+Complex.regularizedHGFun_le_exp_of_one_le_re
+Complex.regularizedHGFun_zero_singleton_eq_mul_add_mul
+Complex.summable_besselJ_mul_pow
+Complex.tsum_besselJ_mul_pow
+Complex.two_mul_deriv_besselJ
+Complex.two_mul_deriv_besselJ_int
+Complex.two_mul_self_mul_besselJ
+Multiset.nnnorm_prod_map
+Multiset.norm_prod_map
+nnnormHom.congr_simp
+normHom.congr_simp

---

No changes to strong technical debt.
No changes to weak technical debt.

Current commit dd9dfb87f3
Reference commit fd634dd297

This script lives in the mathlib-ci repository. To run it locally, from your mathlib4 directory:

git clone https://github.com/leanprover-community/mathlib-ci.git ../mathlib-ci
../mathlib-ci/scripts/reporting/technical-debt-metrics.py 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).

[mathlib-dependent-issues]

This PR/issue depends on:

• feat(Analysis/SpecialFunctions): derivative of Bessel function of the first kind #42825
• feat(Analysis/Normed): norm and Multiset.prod commute #43979
  By Dependent Issues (🤖). Happy coding!

[mathlib-bors]

This pull request is now in draft mode. No active bors state needed cleanup.

While this PR remains draft, bors will ignore commands on this PR. Mark it ready for review before using commands like bors r+ or bors try.