[Help-gsl] Re: A few questions about finding all zeros of Hermite polynomial

[Richard Mathar]

On behalf of
http://lists.gnu.org/archive/html/help-gsl/2007-11/msg00046.html
one may try
http://www.strw.leidenuniv.nl/~mathar/progs/LagZero.c , which is stable
at least up to order 70:

LagZero -H 70

1.3228598727031574e-01 2.5999310620316057e-01
3.9692367564298847e-01 2.2612844383734487e-01
6.6175893081256665e-01 1.7101015293604357e-01
9.2692488970661668e-01 1.1238816501981314e-01
1.1925568563654070e+00 6.4133640985944609e-02
1.4587932269483981e+00 3.1741278188268586e-02
1.7257764756009522e+00 1.3605327567850874e-02
1.9936542226231453e+00 5.0416367534667035e-03
2.2625804097899471e+00 1.6117354139288814e-03
2.5327166122907285e+00 4.4340001998899038e-04
2.8042335229302875e+00 1.0466998173739962e-04
3.0773126524497556e+00 2.1131030668113294e-05
3.3521483007723556e+00 3.6344339797629628e-06
3.6289498686372545e+00 5.3018786512204394e-07
3.9079445988680894e+00 6.5231229900550627e-08
4.1893808634925742e+00 6.7512636627769693e-09
4.4735321501381859e+00 5.8035068367103955e-10
4.7607019531713526e+00 4.1960322961834483e-11
5.0512298489716008e+00 2.3226527644617368e-12
5.3454991415732511e+00 1.1337324365805188e-13
5.6439466223452390e+00 4.8823220258731440e-15
5.9470752244713703e+00 1.0699772209822617e-16
6.2554707188783167e+00 3.0179374416964878e-18
6.5698241787566669e+00 7.8984096655761513e-20
6.8909628903904032e+00 8.1334799725562477e-22
7.2198940023018823e+00 7.0709229525752888e-24
7.5578680649896146e+00 6.5772909721107653e-26
7.9064749419687788e+00 1.9232964004346795e-28
8.2677951152318077e+00 6.9659652066346418e-31
8.6446518655005509e+00 1.4032794077167204e-33
9.0410623133341144e+00 1.2827806369087580e-36
9.4631239608462074e+00 5.5891637121667083e-40
9.9210064725726355e+00 8.6319853950662405e-44
1.0434459776321239e+01 2.8687890534653838e-48
1.1055240743138121e+01 5.9856206004921644e-54

If this is just to be run once, an alternative is to use either PARI or
Maple to produce the list of all the zeros, and to generate a big table of
these that can be statically added to the application coding.

-- 
Richard J Mathar
http://www.strw.leidenuniv.nl/~mathar