I want to find out when a function has a real root.
I first made a RegionPlot3D
when the function is zero.
Manipulate[
RegionPlot3D[(A*x)^(1 - s) -
NSum[B^(n)*(x^((1 - s)*z^n))*
Exp[(1 - z^(2 n))*(1 - s)^2*v^2/(2*(1 - z^2))], {n, 1, Infinity}] -
NSum[B^(n)*(y^((1 - s)*q^n))*
Exp[(1 - q^(2 n))*(1 - s)^2*p^2/(2*(1 - q^2))], {n, 1, Infinity}] == 0,
{x, 0.95, 1.05}, {y, 0.95, 1.05}, {z, 0.95, 0.99}],
{q, {0.95}},
{v,{0.0035}},
{p, {0.0035}},
{s,{2}},
{B,{0.95}},
{A,{0.96}}]
I got a blank cubic.
As a check I plotted the function in 2D. However, the 2D plot shows that the function has a zero when M = x =0.9528
and K = y = 1.0396
.
Manipulate[
Plot[(A*M)^(1 - s) +
NSum[(B^n*(K^((1 - s)*(q)^n))*
Exp[(1 - (q)^(2*n))*((p)^2)*(1 - s)^2/(2*(1 - (q)^2))]), {n, 1, Infinity}] -
NSum[(B^n*(M^((1 - s)*r^n))*
Exp[(1 - r^(2*n))*(v^2)*(1 - s)^2/(2*(1 - r^2))]), {n, 1, Infinity}] ,
{r, 0.95, 0.99}],
{q, {0.95}},
{M, {0.9528}},
{K, {1.0396}},
{v,{0.0035}},
{p, {0.0035}},
{s, {2}},
{B, {0.95}},
{A, {0.96}}]
Further, I tried to zoom into the area where the 2D plot shows that a zero may exist and found that it is no longer a monotonic function (its zigzag and crosses the horizontal axis many times).
What do I make of this? Does it mean that a zero exists in the complex plane?
B
seems to be raised to a different pawer in the sum between the two expressions. $\endgroup$