9
You can see why when you break it up. Since you use 1.1 then Mathematica evaluated it numerically.
Compare
v = 1 + I
a = Abs[v]
b = Exp[I Arg[v]]
a*b
With
v = 1.10 + I
a = Abs[v]
b = Exp[I Arg[v]]
a*b
You see that Exp[I Arg[v]] now is 0.73994 + 0.672673 I
To keep things nice, as your first example, use exact number
v = 11/10 + I
a = Abs[v]
b = Exp[I Arg[...
3
What can I do to have a sequences of j and n in Plot function without
specifying paticular numbers
If I understand you right, you can first generate the j,n data first
Clear["Global`*"]
data = Flatten[Table[{j, n}, {j, 3}, {n, 3}], 1]
Now generate the functions for each j,n above
f[j_, n_, x_] :=
Piecewise[{{0, j/2^n <= x && x <= (...
2
You can use Fold and switch i and v in your definition of h ...
h[v_, i_] := ...
Fold[h, v, Range[3]]
(* h[h[h[v, 1], 2], 3] *)
... or switch the order directly in Fold.
h[i_, v_] := ...
Fold[h[#2, #1] &, v, Range[3]]
(* h[3, h[2, h[1, v]]] *)
1
We can test the result by uses Newton-Leibniz formula.
f = Integrate[x/(-x^2 + a x + b)^(1/2), x];
expr2 = (f /. x -> Sqrt[R^2 + b]) - (f /. x -> Sqrt[b])
expr1 = Integrate[
x/(-x^2 + a x + b)^(1/2), {x, Sqrt[b], Sqrt[R^2 + b]},
Assumptions -> {a > 0, b > 0, R > 0}]
FullSimplify[expr1 == expr2, Assumptions -> {a > 0, b > 0, R &...
1
Clear["Global`*"]
Include the assumption that R is real.
Assuming[{a > 0, b > 0, Element[R, Reals]},
Integrate[x/(-x^2 + a x + b)^(1/2), {x, Sqrt[b], Sqrt[R^2 + b]}] //
FullSimplify]
1
as far as I know, you can't define functions inside Table or a Do loop. Unless there is a hack to do it.
My main objective is to define and use a family of functions
Why not define the function F itself to take its id as part of the definition? As a meta function. Like this
F[i_,Subscript[β_,i_],Subscript[b_,i_]]:=Subscript[β,i]+i+i*Subscript[b,i]
And ...
1
Here's how I would write your example, in a way that "jibes" with Mathematica.
(* Define the functions in terms of parameters *)
fun1[a_, b_][c_][x_] := a + b x + c
fun2[a_, b_][c_][x_] := b + a x + c
fun3[a_, b_][c_][x_] := fun1[a, b][c][x] + fun2[a, b][c][x]
(* Specify the parameters' values *)
a = 1; b = 2; c = {1, 4, 10};
(* Rather than loop, ...
1
Maybe the following? I didn't understand all the extra variables, so I stripped down the code more. In a complicated case, you might need Dynamic@Refresh instead of just Dynamic; see What is the point of Refresh if Dynamic has an UpdateInterval option? and related Q&A on Refresh. You'd probably have to put the output in a docked cell, since the FE ...
Only top voted, non community-wiki answers of a minimum length are eligible