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hermite

hermite (0.5,-1);

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hermite

numerator(hermite(3, ...

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hermite

hermite (3,5);

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hermite

hermite (2,-0.707107);

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hermite

hermite (2,-1);

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hermite

hermite(3, 3/22);

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hermite

hermite (1/2,-1);

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hermite-makelist-num

makelist(num(hermite(...

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hermite-num

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

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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
hermite (1/2,-1);
(%o1)                              H   (- 1)
                                    1/2
(%i2) 

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