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Data retrieval process in hetero-associative memory, extended to higher order correlations, has been formulated into a functional in terms of Hamming distance between the memorized keys and an applied input key. In this paradigm, we show that the functional representation already presented is the exactly same to the functional representation in terms of the Krawtchouk polynomial, and further, the memory capacity of associative memory is also described by a functional form in terms of the Krawtchouk polynomial. The resultant functional representation on memory capacity is of wide generality and it is verified that it includes the well-known formula on memory capacity of the Hopfield auto-associative memory as a special case.