### Related

##### delta-integrate-plot2d-solve-subst

M:M1-M1/L*x;

theta : integrate(M/E...

delta : integrate(the...

Calculate

##### delta-solve

eq1:-((r+lamda)*uh+th...

solve(eq1,kappa);

Calculate

##### delta-sum

f(x):=-x^2+4;

delta:(0+2)/4;

f(0.5)+f(1)+f(1.5)+f(2);

Calculate

##### delta-kill-ratcoef-solve-subst

kill(all);

retta : y - yp - m*(x...

ellisse : x^2/a^2 + y...

Calculate

##### delta-diff-exp-laplace-sin

laplace (exp (2*t + a...

laplace ('diff (f (x...

diff (diff (delta (t...

Calculate

##### delta-kill-linsolve

kill(eq1,eq1,eq3,eq4,...

eq1:x=t;

eq:y=x+t;

Calculate

##### delta

(((1/2)*Dist)^(-delta...

Calculate

##### delta-linsolve

eq1:R=(x^2+y^2)/(2*x);

eq2:y/(R-x) = (R*d+l*...

eq3:(del-x)^2+(l+d-y)...

Calculate

##### delta-sin

delta(x1-x2)*sin(x1)*...

Calculate

v1:[1,2,1,3];

v2:[2,5,3,1];

v3:[1,1,2,2];

Calculate

### delta

Run Example
```(%i1)remvalue(n,z);
(%o1)                           [false, false]
(%i2) matchdeclare(a,lambda([x],freeof(x,n)));
(%o2)                                done
(%i3) matchdeclare(b,lambda([x],freeof(x,n) and integerp(x) and x>
0));
(%o3)                                done
(%i4) matchdeclare(f,all);
(%o4)                                done
(%i5) matchdeclare(g,lambda([x],freeof(n-1,x)));
(%o5)                                done
(%i6) defrule(r1,zt(1,n,z),z/(z-1));
z
(%o6)                      r1 : zt(1, n, z) -> -----
z - 1
(%i7) defrule(r2,zt(n,n,z),z/(z-1)^2);
z
(%o7)                    r2 : zt(n, n, z) -> --------
2
(z - 1)
(%i8) defrule(r3,zt(1/n,n,z),log(z/(z-1)));
1                 z
(%o8)                   r3 : zt(-, n, z) -> log(-----)
n               z - 1
(%i9) defrule(r4,zt(a^n,n,z),z/(z-a));
n             z
(%o9)                     r4 : zt(a , n, z) -> -----
z - a
(%i10) defrule(r5,zt(a^(n-1),n,z),1/(z-a));
n - 1             1
(%o10)                  r5 : zt(a     , n, z) -> -----
z - a
(%i11) defrule(r6,zt(binomial(n,b),n,z),z/(z-1)^(b+1));
- b - 1
(%o11)         r6 : zt(binomial(n, b), n, z) -> (z - 1)        z
(%i12) defrule(r7,zt(n^b,n,z),block([tmp:z/(z-1)],  for i:1 thru b do tmp:-z*diff(tmp,z),  factor(tmp)));
b                          z
(%o12) r7 : zt(n , n, z) -> block([tmp : -----],
z - 1
for i thru b do tmp : - diff(tmp, z) z, factor(tmp))
(%i13) defrule(r8,zt(sin(a*n),n,z),z*'sin(a)/((z^2-2*z*'cos(a)+1)));
sin(a) z
(%o13)          r8 : zt(sin(a n), n, z) -> -------------------
2
z  - 2 cos(a) z + 1
(%i14) defrule(r9,zt(cos(a*n),n,z),z*(z-'cos(a))/(z^2-2*z*'cos(a)+1));
z (z - cos(a))
(%o14)          r9 : zt(cos(a n), n, z) -> -------------------
2
z  - 2 cos(a) z + 1
(%i15) defrule(r10,zt(kron_delta(b,n),n,z),1/z^b);
1
(%o15)              r10 : zt(kron_delta(b, n), n, z) -> --
b
z
(%i16) defrule(r11,zt(a^n*f,n,z),'subst(z/a,z,ztrans(f,n,z)));
n                        z
(%o16)     r11 : zt(a  f, n, z) -> substitute(-, z, ztrans(f, n, z))
a
(%i17) defrule(r12,zt(n^b*g,n,z),block([tmp:ztrans(g,n,z)],  for i:1 thru b do tmp:-z*'diff(tmp,z),  return(tmp)));
b
(%o17) r12 : zt(g n , n, z) -> block([tmp : ztrans(g, n, z)],
dtmp
for i thru b do tmp : - ---- z, return(tmp))
dz
(%i18) defrule(r13,zt(exp(-a*n),n,z),z/(z-exp(-a)));
- a n               z
(%o18)               r13 : zt(%e     , n, z) -> ---------
- a
z - %e
(%i19) defrule(r14,zt(f(n-m),n,z),z^(-m)*ztrans(f(n),n,z));
ztrans(f(n), n, z)
(%o19)          r14 : zt(f(n - m), n, z) -> ------------------
m
z
(%i20) declare(zt,linear);
(%o20)                               done
(%i21) ztrans1(e):=apply1(e,r1,r2,r3,r4,r5,r6,r7,r8,r9,r10,r11,r12,r13,r14);
(%o21) ztrans1(e) := apply1(e, r1, r2, r3, r4, r5, r6, r7, r8, r9, r10, r11,
r12, r13, r14)
(%i22) ztrans(f,n,z):=ev(ztrans1(zt(f,n,z)),diff,subst);
(%o22)     ztrans(f, n, z) := ev(ztrans1(zt(f, n, z)), diff, subst)
(%i23) defrule(ir1,izt(z/(z-a),z,n),a^n);
z              n
(%o23)                   ir1 : izt(-----, z, n) -> a
z - a
(%i24) defrule(ir2,izt(1/(z-a),z,n),a^(n-1));
1              n - 1
(%o24)                 ir2 : izt(-----, z, n) -> a
z - a
(%i25) declare(izt,linear);
(%o25)                               done
(%i26) invztrans1(e):=apply1(e,ir1,ir2);
(%o26)               invztrans1(e) := apply1(e, ir1, ir2)
(%i27) invztrans(f,z,n):=invztrans1(izt(f,z,n));
(%o27)          invztrans(f, z, n) := invztrans1(izt(f, z, n))
(%i28) ztrans(1,n,z);
z
(%o28)                               -----
z - 1
(%i29) ztrans(a,n,z);
a z
(%o29)                               -----
z - 1
(%i30) expand(ztrans((-1)^n,n,z));
z
(%o30)                               -----
z + 1
(%i31) ztrans(n,n,z);
z
(%o31)                             --------
2
(z - 1)
(%i32) ztrans(n^2,n,z);
z (z + 1)
(%o32)                             ---------
3
(z - 1)
(%i33) ztrans(a^(n-1),n,z);
1
(%o33)                               -----
z - a
(%i34) factor(ztrans(a^(n-1)+n^2,n,z));
3      2      2
2 z  - a z  - 2 z  - a z + 3 z - 1
(%o34)                ----------------------------------
3
(z - 1)  (z - a)
(%i35) ```
Run Example
```f(x,y,z):= 3*x*y+2*(2*x*z+2*y*z);
(%o1)               f(x, y, z) := 3 x y + 2 (2 x z + 2 y z)
(%i2) 'CX(x,y,z)=CX:diff(f(x,y,z),x,1);
(%o2)                       CX(x, y, z) = 4 z + 3 y
(%i3) %Delta(x)=delta:3/12;
1
(%o3)                            %Delta(x) = -
4
(%i4) limit(1/x,x,0);
(%o4)                              infinity
(%i5) ```
Run Example
```l:1;
(%o1)                                  1
(%i2) a:1;
(%o2)                                  1
(%i3) c:l/10;
1
(%o3)                                 --
10
(%i4) delta:0.1;
(%o4)                                 0.1
(%i5) v:1;
(%o5)                                  1
(%i6) (2/l)*integrate((v*cos((x-c)/delta)*%pi/2),x,(c-delta),(c+delta));

rat: replaced 0.2 by 1/5 = 0.2

rat: replaced 0.0 by 0/1 = 0.0

rat: replaced 0.2 by 1/5 = 0.2

rat: replaced 0.2 by 1/5 = 0.2

rat: replaced 10.0 by 10/1 = 10.0

rat: replaced 10.0 by 10/1 = 10.0

rat: replaced 0.2 by 1/5 = 0.2

rat: replaced 0.0 by 0/1 = 0.0

rat: replaced 0.2 by 1/5 = 0.2

rat: replaced 0.2 by 1/5 = 0.2

rat: replaced 10.0 by 10/1 = 10.0

rat: replaced -0.08414709848079 by -5558/66051 = -0.08414709845422

rat: replaced 0.08414709848079 by 5558/66051 = 0.084147098454225
11116 %pi
(%o6)                              ---------
66051
(%i7) psin:%o6;
(%o7)             u:sum(psin*%pi*n*x/l)*sin(%pi*n*a*t/l)*(%pi*n*a/l)^(-1),n,1,50);
```

Help for Delta