  In 1+1 dimensional hydrodynamics originally proposed by Landau, we derive a
new potential and distribution function including Heaviside function and
investigate its mathematical and physical properties. Using the original
distribution derived by Landau, a distribution function found by Srivastava et
al., our distribution function, and the Gaussian distribution proposed by
Carruthers et al., we analyze the data of the rapidity distribution on charged
pions and K mesons at RHIC energies (sqrt(s_NN) = 62.4 GeV and 200 GeV). Three
distributions derived from the hydrodynamics show almost the same chi-squared
values provided the CERN MINUIT is used. We know that our calculations of
hadron's distribution do not strongly depend on the range of integration of
fluid rapidity, contrary to that of Srivastava et al. Finally the roles of the
Heaviside function in concrete analyses of data are investigated.
