Nonexistence of Chebyshev-type quadratures on infinite intervals

Walter Gautschi
1975 Mathematics of Computation  
Quadrature rules on semi-infinite and infinite intervals are considered involving weight functions of the Laguerre and Hermite type. It is shown that such quadrature rules cannot have equal coefficients and real nodes unless the algebraic degree of accuracy is severely limited.
doi:10.1090/s0025-5718-1975-0368392-3 fatcat:uobb5ps2gzh2rfjxoizyivssta