1,8

Because of error functions in the result where constants should be

this is a difficult calculation.

Probably the wrong approach, but it is my best effort at getting

Gaussian normal type functions to give integers. There has got to be a better way than this:

maybe a conformal transform of the known Chebyshev Integration polynomials?

No recurrence formula was found for these polynomial, so they are probably wrong.

Row sums are:

{1, 1, 0, -3, 4, 17, 32, -51, 0, 793}

page 8 and pages 42 - 43 : Harry Hochstadt, The Functions of Mathematical Physics, Dover, New York, 1986

P(x, n) = x*P(x, n - 1) - n*P(x, n - 2); L(x,n)=Integrate[Exp[y^2/4]*p(y,n-1),{y,-Infinity,x}]/(-2*Exp[ -x^2/4]) Here the weight function is taken as the square root of the Hermite weight function Exp[ -x^2/2] and then divided out of the end result.

{1},

{0, 1},

{-1, 0, 1},

{-1, -3, 0, 1},

{9, 0, -6, 0, 1},

{-1, 27, 0, -10, 0, 1},

{-19, 0, 65, 0, -15, 0, 1},

{-1, -165, 0, 135, 0, -21, 0,1},

{399, 0, -624, 0, 252, 0, -28, 0, 1},

{-1, 2145, 0, -1750, 0, 434, 0, -36, 0, 1}

Cf. A137286.

Adjacent sequences: A136236 A136237 A136238 this_sequence A136240 A136241 A136242

Sequence in context: A020816 A099097 A152150 this_sequence A058175 A112906 A137375

uned,tabl,sign

Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Mar 16 2008