fix(uncertainbessels): update documentation for clarity and consistency in mathematical notation

Author: amaurigmartins

docs/src/refs.bib

@@ -1,7 +1,7 @@
 @misc{NIST:DLMF,
 key = {DLMF},
 title = {NIST Digital Library of Mathematical Functions},
-editor = {Olver, F. W. J. and Olde Daalhuis, A. B. and Lozier, D. W. and Schneider, B. I. and Boisvert, R. F. and Clark, C. W. and Miller, B. R. and Saunders, B. V. and Cohl, H. S. and McClain, M. A.},
+note = {Olver, F. W. J. and Olde Daalhuis, A. B. and Lozier, D. W. and Schneider, B. I. and Boisvert, R. F. and Clark, C. W. and Miller, B. R. and Saunders, B. V. and Cohl, H. S. and McClain, M. A., eds.},
 year = {2025},
 institution = {National Institute of Standards and Technology (NIST)},
 howpublished = {[{https://dlmf.nist.gov/}]({https://dlmf.nist.gov/}), Release 1.2.4 of 2025-03-15},

src/uncertainbessels/UncertainBessels.jl

@@ -6,14 +6,13 @@ Uncertainty-aware wrappers for Bessel functions.
 [`UncertainBessels`](@ref) lifts selected functions from `SpecialFunctions` so they accept
 `Measurement` and `Complex{Measurement}` inputs. The wrapper evaluates the
 underlying function at the nominal complex argument and propagates uncertainty
-via first-order finite differences using the four partial derivatives ``\\frac{\\partial \\Re f}{\\partial x}, \\frac{\\partial \\Re f}{\\partial y}, \\frac{\\partial \\Im f}{\\partial x}, \\frac{\\partial \\Im f}{\\partial y}`` with ``x = \\Re z`` and ``y = \\Im z``. No new Bessel algorithms are implemented:
-for plain numeric inputs, results and numerical behaviour are those of
+via first-order finite differences using the four partial derivatives ``\\frac{\\partial \\mathrm{Re} \\, f}{\\partial x}, \\frac{\\partial \\mathrm{Re} \\, f}{\\partial y}, \\frac{\\partial \\mathrm{Im} \\, f}{\\partial x}, \\frac{\\partial \\mathrm{Im} \\, f}{\\partial y}`` with ``x = \\mathrm{Re}(z)`` and ``y = \\mathrm{Im}(z)``. No new Bessel algorithms are implemented: for plain numeric inputs, results and numerical behaviour are those of
 `SpecialFunctions`.
 
 Numerical scaling (as defined by `SpecialFunctions`) is supported for the
 “x” variants (e.g. `besselix`, `besselkx`, `besseljx`, …) to improve stability
 for large or complex arguments. In particular, the modified functions use
-exponential factors to temper growth along ``\\Re z`` (e.g. ``I_\\nu`` and ``K_\\nu``);
+exponential factors to temper growth along ``\\mathrm{Re}(z)`` (e.g. ``I_\\nu`` and ``K_\\nu``);
 other scaled variants follow conventions in `SpecialFunctions` and DLMF guidance
 for complex arguments. See [NIST:DLMF](@cite) and [6897971](@cite).
 
@@ -22,12 +21,13 @@ for complex arguments. See [NIST:DLMF](@cite) and [6897971](@cite).
 - Thin, uncertainty-aware wrappers around `SpecialFunctions` (`besselj`, `bessely`,
   `besseli`, `besselk`, `besselh`) and their scaled counterparts (`…x`).
 - For `Complex{Measurement}` inputs, uncertainty is propagated using the 4-component
-  gradient with respect to ``\\Re z`` and ``\\Im z``.
+  gradient with respect to ``\\mathrm{Re}(z)`` and ``\\mathrm{Im}(z)``.
 - For `Measurement` (real) inputs, a 1-D finite-difference derivative is used.
 - No change in semantics for `Real`/`Complex` inputs: calls delegate to `SpecialFunctions`.
 
 # Dependencies
 
+- `SpecialFunctions`
 $(IMPORTS)
 
 # Exports
@@ -37,6 +37,8 @@ $(EXPORTS)
 # Usage
 
 ```julia
+# do not import SpecialFunctions directly
+using LineCableModels.UncertainBessels 
 z = complex(1.0, 1.0 ± 0.5)
 J0_cpl = besselj(0, z)		    # Complex{Measurement}
 J0_nom = besselj(0, value(z))  	# nominal comparison
@@ -45,7 +47,7 @@ I1 = besselix(1, z)           	# scaled I1 with uncertainty
 
 # Numerical notes
 
-- Scaled modified Bessels remove large exponential factors along ``\\Re z`` (e.g., ``I_\\nu`` and ``K_\\nu`` are scaled by opposite signs of ``|\\Re z|``), improving conditioning. Scaled forms for the other families follow the definitions in `SpecialFunctions` and DLMF.
+- Scaled modified Bessels remove large exponential factors along ``\\mathrm{Re}(z)`` (e.g., ``I_\\nu`` and ``K_\\nu`` are scaled by opposite signs of ``|\\mathrm{Re}(z)|``), improving conditioning. Scaled forms for the other families follow the definitions in `SpecialFunctions` and DLMF.
 - Uncertainty propagation is first order (linearization at the nominal point).
   Large uncertainties or strong nonlinearity may reduce accuracy.