A note on Hansen's coefficients in satellite theory

General formulas for Hansen's coefficients in satellite theory are derived along with expressions for the eccentricity functions G and H. Recurrence relations for the eccentricity functions and their derivatives are obtained which are valid for all values of the parameter p. It is noted that the recurrence relations obtained by Challe and Laclaverie (1969) as well as by Balmino (1973) do not satisfy certain parity conditions and therefore involve coefficients outside the range of usage.