Absorption cross section of scalar field in supergravity background

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 modi fied Mathieu equation. In the following the absorption rate of the scalar b y a D3 brane in ten dimensions is calculated in terms of modified Mathieu f unctions of the first kind, using standard Mathieu coefficients. The relati on of the latter to Dougall coefficients (used by others) is investigated. The S-matrix obtained in terms of modified Mathieu functions of the first k ind is easily evaluated if known rapidly convergent low energy expansions o f these in terms of products of Bessel functions are used. Leading order te rms, including the interesting logarithmic contributions, can be obtained a nalytically. (C) 2000 Elsevier Science B.V. All rights reserved.