  It has recently been shown that the equation of motion of a massless scalar
field in the background of some specific p branes can be reduced to a modified
Mathieu equation. In the following the absorption rate of the scalar by a D3
brane in ten dimensions is calculated in terms of modified Mathieu functions of
the first kind, using standard Mathieu coefficients. The relation of the latter
to Dougall coefficients (used by others) is investigated. The S-matrix obtained
in terms of modified Mathieu functions of the first kind is easily evaluated if
known rapidly convergent low energy expansions of these in terms of products of
Bessel functions are used. Leading order terms, including the interesting
logarithmic contributions, can be obtained analytically.
