AbstractIn this paper first we establish six recurrence relations for the H‐function with the help of certain formulae concerning generalized BESSEL function. Later on, we obtain recurrence relations for MEIJER'S G‐function, GAUSS'S hypergeometric function and BESSEL function. On account of the general character of the H‐function, recurrence relations for other special functions can also be obtained as special cases of our results. Two well‐known results obtained earlier by Prof. MEIJER follow as special cases of our findings.