### Related

##### hermite

hermite(3, 3/22);

Calculate

##### hermite

hermite (1/2,-1);

Calculate

##### hermite-num

num(hermite(3, 3/22));

Calculate

##### hermite-makelist-num

makelist(num(hermite(...

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##### hermite

hermite (2,-0.7);

Calculate

##### hermite

numerator(hermite(3, ...

Calculate

hermite(5,x);

Calculate

hermite(5,x);

Calculate

##### hermite

hermite (2,-0.7);

Calculate

hermite(5,x);

Calculate

### hermite

Run Example
(%i1)num(hermite(3, 3/22));
(%o1)                               - 2151
(%i2)
Run Example
sum(t^n/n! * diff(diff(%e^(x*y*t), x, n), y, n), n, 0, inf), simpsum=true;
2 n
n   d         t x y
inf   t  (------- (%e     ))
====        n   n
\         dx  dy
(%o1)                     >    ----------------------
/               n!
====
n = 0
(%i2) sum(t^n/n! * t^n * hermite(t*x*y, n), n, 0, inf), simpsum=true;
inf    2 n
====  t    H     (n)
\           t x y
(%o2)                         >    --------------
/           n!
====
n = 0
(%i3) diff(diff(%e^(x*y*t), x, 1), y, 1);
2       t x y       t x y
(%o3)                     t  x y %e      + t %e
(%i4) diff(diff(%e^(x*y*t), x, 2), y, 2);
4  2  2   t x y      3       t x y      2   t x y
(%o4)         t  x  y  %e      + 4 t  x y %e      + 2 t  %e
(%i5) diff(diff(%e^(x*y*t), x, 3), y, 3);
6  3  3   t x y      5  2  2   t x y       4       t x y      3   t x y
(%o5) t  x  y  %e      + 9 t  x  y  %e      + 18 t  x y %e      + 6 t  %e
(%i6)
Run Example
f(x) := exp(-(x^2)/2)/sqrt(2*%pi);
2
- x
exp(----)
2
(%o1)                         f(x) := -----------
sqrt(2 %pi)
(%i2) integrate(hermite (3, x)*f(x),x,-inf,inf);
(%o2)                                  0
(%i3)

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