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use the formula provided in

http://en.wikipedia.org/wiki/Hermite_polynomials

and run in Maple

Restart;
with(SumTools):
Hn := n!*Summation(((-1)^(n/2-l))/((2*l)!*(n/2-l)!)*((2*x)^(2*l)),l=0..n/2);
genfun := Summation(Hn/n!*z^n,n=0..infinity);

but result is not exp(2*x*t - t^2)

Following Christopher2222 request, I wrote the following procedures for "exact" cubic Hermite spline interpolation,

p:=proc(x0,p0,m0,x1,p1,m1,x)
local t,d;
d:=x1-x0;
t:=(x-x0)/d;
p0+(d*m0+(3*(p1-p0)-d*(2*m0+m1)+(2*(p0-p1)+d*(m0+m1))*t)*t)*t
end:

pb:=proc(x0,p0,x1,p1,m1,x)
local t,d;
d:=x1-x0;
t:=(x-x0)/d;
p0+(2*(p1-p0)-d*m1+(p0-p1+d*m1)*t)*t
end:

pe:=proc(x0,p0,m0,x1,p1,x...
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