These are (x,y), both positive and y is below the falling diagnonal + 1, 
i.e. { (x,y)| 0 <= x, 0 <= y, y <= -x+1 } as indicator.

To see this set z=0 and your equation becomes 
(1-m-2*e*(1-c^2)^(1/2)*r^(1/2)) * H(0) = 0,

But your parameters do not satisfy the relation,
so H(0) = 0 and the equation then says H(z)=0

To see this set z=0 and your equation becomes 
(1-m-2*e*(1-c^2)^(1/2)*r^(1/2)) * H(0) = 0,

But your parameters do not satisfy the relation,
so H(0) = 0 and the equation then says H(z)=0

Yes, that's what I said: 

It is a (hyper-) surface in the space of variables, in your example with dim=2 it
is a curve.

Note that for correlation = 0 Maple can solve the double integral symbolically:

  eval(bipdf, [sigma[1] = 1, sigma[2] = 1, mu[1] = 0, mu[2] = 0, rho = 0]);
  int(int(%, x[2] = -infinity .. y2), x[1] = -infinity .. y1);
  F := simplify(%, size);

      F := 1/4*(1+erf(1/2*y2*2^(1/2)))*(1+erf(1/2*2^(1/2)*y1))

which is the product of 2 cdf normals, an analytic function of 2 variables, y1 and y2.

For given p the equation p = F(y1,y2) defines a curve in C^2, you want the real
points only.

Guess that Maple can not give a parametric solution (suggestion for the example:
H:= inverse cdf normal and p = F(y1,y2) = u*v, something hyperbolic).


Edited: I do not understand why the point ~ (1,1) is 'optimal' for you and
what is the meaning of the falling line (why that shift by -1.6?). 
If you mean y1=y2 and on the curve, then -0.7600685751... is the value.
Note that the boundaries vertical and horizontal are -1.64485362695147,
beyond there is no solution in the Reals.

Yes, that's what I said: 

It is a (hyper-) surface in the space of variables, in your example with dim=2 it
is a curve.

Note that for correlation = 0 Maple can solve the double integral symbolically:

  eval(bipdf, [sigma[1] = 1, sigma[2] = 1, mu[1] = 0, mu[2] = 0, rho = 0]);
  int(int(%, x[2] = -infinity .. y2), x[1] = -infinity .. y1);
  F := simplify(%, size);

      F := 1/4*(1+erf(1/2*y2*2^(1/2)))*(1+erf(1/2*2^(1/2)*y1))

which is the product of 2 cdf normals, an analytic function of 2 variables, y1 and y2.

For given p the equation p = F(y1,y2) defines a curve in C^2, you want the real
points only.

Guess that Maple can not give a parametric solution (suggestion for the example:
H:= inverse cdf normal and p = F(y1,y2) = u*v, something hyperbolic).


Edited: I do not understand why the point ~ (1,1) is 'optimal' for you and
what is the meaning of the falling line (why that shift by -1.6?). 
If you mean y1=y2 and on the curve, then -0.7600685751... is the value.
Note that the boundaries vertical and horizontal are -1.64485362695147,
beyond there is no solution in the Reals.

Roughly Maple thinks that t[a] is a special case of t, while you may have
in mind just the fact it is a constant related to t (in what sense ever) and
that this is obvious, since there is to variable t.

That's why Markiyan Hirnyk used some z or tau to tell the machine.

Best is to avoid indexed variables if possible, in my humble opinion
(though it is possible, but with care).

Or for systematics use a Greek symbol if you otherwise have Latin once.

Roughly Maple thinks that t[a] is a special case of t, while you may have
in mind just the fact it is a constant related to t (in what sense ever) and
that this is obvious, since there is to variable t.

That's why Markiyan Hirnyk used some z or tau to tell the machine.

Best is to avoid indexed variables if possible, in my humble opinion
(though it is possible, but with care).

Or for systematics use a Greek symbol if you otherwise have Latin once.

I cleaned up the sheet, computational time now is only some milli seconds

Ooura_intde_oscillat.mws

I cleaned up the sheet, computational time now is only some milli seconds

Ooura_intde_oscillat.mws

I think there are 2 reasons:

One is (my) posting in fixed font (named 'preformatted' in the board editor), 
which prevents line breaks - this is where the poster has to take some care.

The other is the layout + functionality of that board and using Firefox.

Besides Robert Israel's way I prefer a different way: zooming in.

That can be done either through the menu bar (view/zoom/ ...)
or more convenient using the key board, pressing the control key and at the
same time the plus key, or for short: <ctrl> + '+'

Not sure, whether it works that way for cyrillic layout.

The result (see below) is, that the 'borders' vanish :-)

I am not sure, whether that is specific for the Firfox version and if there are
side effects (as I do not allow all scripts of the board software, see bottom
of the screen shot, below):

####################################################

##########################################

Looked at it again. The best I could do is in the attached sheet Hirnyk_int_128619.mws,
but the power series is not proved (the trailing terms are missing of course, and more).

I simply miss a criterion ...

Hirnyk_int_12861.mws

Looked at it again. The best I could do is in the attached sheet Hirnyk_int_128619.mws,
but the power series is not proved (the trailing terms are missing of course, and more).

I simply miss a criterion ...

Hirnyk_int_12861.mws

here the problem is 'osciallation'

but as the poster does not answer since 2 days,
it seems to be not very important for him :-)

here the problem is 'osciallation'

but as the poster does not answer since 2 days,
it seems to be not very important for him :-)

additionally one has to care for upper/lower case for n resp N