text: #ifndef STAN_MATH_PRIM_PROB_CHI_SQUARE_LPDF_HPP
  #define STAN_MATH_PRIM_PROB_CHI_SQUARE_LPDF_HPP
  
  #include <stan/math/prim/meta.hpp>
  #include <stan/math/prim/err.hpp>
  #include <stan/math/prim/fun/as_column_vector_or_scalar.hpp>
  #include <stan/math/prim/fun/as_value_column_array_or_scalar.hpp>
  #include <stan/math/prim/fun/constants.hpp>
  #include <stan/math/prim/fun/digamma.hpp>
  #include <stan/math/prim/fun/lgamma.hpp>
  #include <stan/math/prim/fun/log.hpp>
  #include <stan/math/prim/fun/max_size.hpp>
  #include <stan/math/prim/fun/size.hpp>
  #include <stan/math/prim/fun/size_zero.hpp>
  #include <stan/math/prim/fun/to_ref.hpp>
  #include <stan/math/prim/fun/value_of.hpp>
  #include <stan/math/prim/functor/operands_and_partials.hpp>
  #include <cmath>
  
  namespace stan {
  namespace math {
  
  /** \ingroup prob_dists
   * The log of a chi-squared density for y with the specified
   * degrees of freedom parameter.
   * The degrees of freedom parameter must be greater than 0.
   * y must be greater than or equal to 0.
   *
   \f{eqnarray*}{
   y &\sim& \chi^2_\nu \\
   \log (p (y \, |\, \nu)) &=& \log \left( \frac{2^{-\nu / 2}}{\Gamma (\nu / 2)}
   y^{\nu / 2 - 1} \exp^{- y / 2} \right) \\
   &=& - \frac{\nu}{2} \log(2) - \log (\Gamma (\nu / 2)) + (\frac{\nu}{2} - 1)
   \log(y) - \frac{y}{2} \\ & & \mathrm{ where } \; y \ge 0 \f}
   *
   * @tparam T_y type of scalar
   * @tparam T_dof type of degrees of freedom
   * @param y A scalar variable.
   * @param nu Degrees of freedom.
   * @throw std::domain_error if nu is not greater than or equal to 0
   * @throw std::domain_error if y is not greater than or equal to 0.
   */
  template <bool propto, typename T_y, typename T_dof,
            require_all_not_nonscalar_prim_or_rev_kernel_expression_t<
                T_y, T_dof>* = nullptr>
  return_type_t<T_y, T_dof> chi_square_lpdf(const T_y& y, const T_dof& nu) {
    using T_partials_return = partials_return_t<T_y, T_dof>;
    using T_partials_array = Eigen::Array<T_partials_return, Eigen::Dynamic, 1>;
    using std::log;
    static const char* function = "chi_square_lpdf";
    using T_y_ref = ref_type_t<T_y>;
    using T_nu_ref = ref_type_t<T_dof>;
    check_consistent_sizes(function, "Random variable", y,
                           "Degrees of freedom parameter", nu);
    T_y_ref y_ref = y;
    T_nu_ref nu_ref = nu;
  
    decltype(auto) y_val = to_ref(as_value_column_array_or_scalar(y_ref));
    decltype(auto) nu_val = to_ref(as_value_column_array_or_scalar(nu_ref));
  
    check_nonnegative(function, "Random variable", y_val);
    check_positive_finite(function, "Degrees of freedom parameter", nu_val);
  
    if (size_zero(y, nu)) {
      return 0;
    }
    if (!include_summand<propto, T_y, T_dof>::value) {
      return 0;
    }
  
    size_t N = max_size(y, nu);
    const auto& log_y = to_ref_if<!is_constant_all<T_dof>::value>(log(y_val));
    const auto& half_nu = to_ref(0.5 * nu_val);
  
    T_partials_return logp(0);
    if (include_summand<propto, T_dof>::value) {
      logp -= sum(nu_val * HALF_LOG_TWO + lgamma(half_nu)) * N / size(nu);
    }
    logp += sum((half_nu - 1.0) * log_y);
  
    if (include_summand<propto, T_y>::value) {
      logp -= 0.5 * sum(y_val) * N / size(y);
    }
  
    operands_and_partials<T_y_ref, T_nu_ref> ops_partials(y_ref, nu_ref);
    if (!is_constant_all<T_y>::value) {
      ops_partials.edge1_.partials_ = (half_nu - 1.0) / y_val - 0.5;
    }
    if (!is_constant_all<T_dof>::value) {
      if (is_vector<T_dof>::value) {
        ops_partials.edge2_.partials_ = forward_as<T_partials_array>(
            (log_y - digamma(half_nu)) * 0.5 - HALF_LOG_TWO);
      } else {
        ops_partials.edge2_.partials_[0]
            = sum(log_y - digamma(half_nu)) * 0.5 - HALF_LOG_TWO * N;
      }
    }
    return ops_partials.build(logp);
  }
  
  template <typename T_y, typename T_dof>
  inline return_type_t<T_y, T_dof> chi_square_lpdf(const T_y& y,
                                                   const T_dof& nu) {
    return chi_square_lpdf<false>(y, nu);
  }
  
  }  // namespace math
  }  // namespace stan
  #endif
  