release/v5.1.0: update release notes

Author: Nick

RELEASE-NOTES.txt

@@ -1,5 +1,27 @@
 Stan Math Library Release Notes
 
+======================================================================
+v5.1.0 (2 September 2025)
+======================================================================
+
+ - Added functions for the embedded Laplace approximation. (#3097, #3209, #3210)
+ - Added new overloads for `sum_to_zero_constrain` and `sum_to_zero_free` that accept Eigen Matrix types. (#3169)
+ - The simplex transform is now defined in terms of the isometric log ratio transform instead of stick breaking. (#3171)
+ - Renamed `hypergeometric_1f0` to `hypergeometric_1F0` for consistency, fixed compilation for `hypergeometric_2f1` with autodiff second argument. (#3165)
+ - Simplified implementation of `chol2inv` using matrix functions. (#3136)
+ - Improved the numerical stability of the gradient calculations for `inv_Phi` and `std_normal_log_qf`. (#3139, #3207)
+ - Simplified vectorisation of `std_normal_lpdf`. (#3140)
+ - Removed redundant computation in `grad_reg_inc_beta`. (#3159)
+ - Updated signature for `apply_scalar_binary` to take the functor as its first argument, instead of the last. (#3156)
+ - Added perfect forwarding to all functions that use the `apply_` family of functors. (#3221, #3228, #3229)
+ - Fixed expression test errors with `poisson_binomial_rng`, added support for row-vector and `std::vector<double>` `theta` arguments for `poisson_binomial`. (#3178)
+ - Updated `inv_logit` to use the logistic function from Eigen. (#3155, #3160)
+ - Update the constraint functions templating to be more flexible. (#3151)
+ - Added ARM64 testing to the Github CI for Windows and Ubuntu (#3177, #3173, #3180, #3174, #3158, #3164)
+ - Disabled Make's implicit rules in our Makefiles. (#3183)
+ - Updated Boost to version 1.87.0 (#3185)
+ - Patched an issue preventing TBB from building with clang 21.1 (#3223)
+
 ======================================================================
 v5.0.0 (10 December 2024)
 ======================================================================