text: #ifndef STAN_MATH_PRIM_SCAL_PROB_BINOMIAL_LPMF_HPP
  #define STAN_MATH_PRIM_SCAL_PROB_BINOMIAL_LPMF_HPP
  
  #include <stan/math/prim/meta.hpp>
  #include <stan/math/prim/scal/err/check_consistent_sizes.hpp>
  #include <stan/math/prim/scal/err/check_bounded.hpp>
  #include <stan/math/prim/scal/err/check_finite.hpp>
  #include <stan/math/prim/scal/err/check_nonnegative.hpp>
  #include <stan/math/prim/scal/fun/size_zero.hpp>
  #include <stan/math/prim/scal/fun/log1m.hpp>
  #include <stan/math/prim/scal/fun/multiply_log.hpp>
  #include <stan/math/prim/scal/fun/value_of.hpp>
  #include <stan/math/prim/scal/fun/binomial_coefficient_log.hpp>
  
  namespace stan {
  namespace math {
  
  /**
   * Returns the log PMF for the binomial distribution evaluated at the
   * specified success, population size, and chance of success. If given
   * containers of matching lengths, returns the log sum of probabilities.
   *
   * @tparam T_n type of successes parameter
   * @tparam T_N type of population size parameter
   * @tparam theta type of chance of success parameter
   * @param n successes parameter
   * @param N population size parameter
   * @param theta chance of success parameter
   * @return log probability or log sum of probabilities
   * @throw std::domain_error if n is negative or greater than N
   * @throw std::domain_error if N is negative
   * @throw std::domain_error if theta is not a valid probability
   * @throw std::invalid_argument if container sizes mismatch
   */
  template <bool propto, typename T_n, typename T_N, typename T_prob>
  return_type_t<T_prob> binomial_lpmf(const T_n& n, const T_N& N,
                                      const T_prob& theta) {
    using T_partials_return = partials_return_t<T_n, T_N, T_prob>;
  
    static const char* function = "binomial_lpmf";
  
    if (size_zero(n, N, theta)) {
      return 0.0;
    }
  
    T_partials_return logp = 0;
    check_bounded(function, "Successes variable", n, 0, N);
    check_nonnegative(function, "Population size parameter", N);
    check_finite(function, "Probability parameter", theta);
    check_bounded(function, "Probability parameter", theta, 0.0, 1.0);
    check_consistent_sizes(function, "Successes variable", n,
                           "Population size parameter", N,
                           "Probability parameter", theta);
  
    if (!include_summand<propto, T_prob>::value) {
      return 0.0;
    }
  
    scalar_seq_view<T_n> n_vec(n);
    scalar_seq_view<T_N> N_vec(N);
    scalar_seq_view<T_prob> theta_vec(theta);
    size_t size = max_size(n, N, theta);
  
    operands_and_partials<T_prob> ops_partials(theta);
  
    if (include_summand<propto>::value) {
      for (size_t i = 0; i < size; ++i) {
        logp += binomial_coefficient_log(N_vec[i], n_vec[i]);
      }
    }
  
    VectorBuilder<true, T_partials_return, T_prob> log1m_theta(length(theta));
    for (size_t i = 0; i < length(theta); ++i) {
      log1m_theta[i] = log1m(value_of(theta_vec[i]));
    }
  
    for (size_t i = 0; i < size; ++i) {
      logp += multiply_log(n_vec[i], value_of(theta_vec[i]))
              + (N_vec[i] - n_vec[i]) * log1m_theta[i];
    }
  
    if (length(theta) == 1) {
      T_partials_return temp1 = 0;
      T_partials_return temp2 = 0;
      for (size_t i = 0; i < size; ++i) {
        temp1 += n_vec[i];
        temp2 += N_vec[i] - n_vec[i];
      }
      if (!is_constant_all<T_prob>::value) {
        ops_partials.edge1_.partials_[0]
            += temp1 / value_of(theta_vec[0])
               - temp2 / (1.0 - value_of(theta_vec[0]));
      }
    } else {
      if (!is_constant_all<T_prob>::value) {
        for (size_t i = 0; i < size; ++i) {
          ops_partials.edge1_.partials_[i]
              += n_vec[i] / value_of(theta_vec[i])
                 - (N_vec[i] - n_vec[i]) / (1.0 - value_of(theta_vec[i]));
        }
      }
    }
  
    return ops_partials.build(logp);
  }
  
  template <typename T_n, typename T_N, typename T_prob>
  inline return_type_t<T_prob> binomial_lpmf(const T_n& n, const T_N& N,
                                             const T_prob& theta) {
    return binomial_lpmf<false>(n, N, theta);
  }
  
  }  // namespace math
  }  // namespace stan
  #endif
  