Error Estimates for Gauss-Laguerre and Gauss-Hermite Quadrature Formulas

  • G. Mastroianni
  • G. Monegato
Part of the ISNM International Series of Numerical Mathematics book series (ISNM, volume 119)


New error estimates are derived for Gauss-Laguerre and Gauss-Hermite m—point quadrature formulas; they are of the type \(O\,({m^{ - r/2}})\,\left\| {{x^{r/2}}} \right.{f^{(r)}}\left. {{x^\alpha }{e^{ - x}}} \right\|\,{L_1}\) and \(O\,({m^{ - r/2}})\,\left\| {{f^{(r)}}} \right.\left. {{e^{ - qx2}}} \right\|{L_1},\,0 <\,q\,1\) respectively, for functions f in suitable function classes.


Orthogonal Polynomial Quadrature Formula Remainder Term Infinite Interval Geometric Convergence 
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Copyright information

© Birkhäuser 1994

Authors and Affiliations

  • G. Mastroianni
    • 1
  • G. Monegato
    • 2
  1. 1.Dipartimento di MatematicaUniversità della BasilicataItalia
  2. 2.Dipartimento di MatematicaPolitecnico di TorinoItalia

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