A transformation formula for a certain Eisenstein series in aerodynamic interference calculations. (English) Zbl 1300.11046
Summary: In 1949, F. W. J. Olver [Q. J. Mech. Appl. Math. 2, 452–457 (1949; Zbl 0034.41302)] established a transformation formula which converts a certain slowly convergent series into a rapidly convergent and easily computable form. The original (double) series occurs in aerodynamic interference calculations, and its numerical estimates have some practical importance. In this paper, the author revisits this double series from the point of view of analytic number theory, and shows the transformation property as a corollary of the Fourier-type expansion of a certain kind of non-holomorphic Eisenstein series by employing Mellin-Barnes integrals.
MSC:
11F37 | Forms of half-integer weight; nonholomorphic modular forms |
40A05 | Convergence and divergence of series and sequences |
76G99 | General aerodynamics and subsonic flows |
76B10 | Jets and cavities, cavitation, free-streamline theory, water-entry problems, airfoil and hydrofoil theory, sloshing |