Bessel関数の零点を標本点に持つ補間および数値積分公式

抄録

An interpolation formula whose abscissae are the zeros of the Bessel functions of integral order is proposed along with its theoretical error analysis. Based on the interpolation formula, two kinds of quadrature formulae of interpolatory type are also proposed : one is for"symmetric integrals"∫^∞_<-∞>f(x)dx and the other for"anti-symmetric integrals"∫^∞_<-∞>sgn x f(x)dx. Both the efficiency of the former quadrature and that of the latter quadrature are studied in theory and in practice, especially compared with the efficiency of the tapezoidal formula.