We have the property such as this
Hypergeometric2F1[a,b,c,z] = (1-z)^(c-b-a)*Hypergeometric2F1[c-a,c-b,c,z]
If we wanted to keep the 2nd term of the hypergeometric function constant, what would the r.h.s. be?
Hypergeometric2F1[a,b,c,z] = something *...
Thank you for checking in Maple. Hmmm... two things
1. Mathematica software sometimes gives erroneous analytic solutions for integration. Do we fall into that kind of error w. Maple sometimes?
2. If the above is analytically correct, can we represent the solution as exponential or trig...
I need to simplify the following if possible
_2F_1(a,b;c;-x^2) - _2F_1(a+1,b+1;c+1;-x^2)
In fact, a= 1/2 and c=3/2 and b>=1. In other words, the difference above that I am interested in is more specifically
_2F_1(.5, b; 1.5; -x^2) - _2F_1(.5+1, b+1...
I would like to generate a similar 3D graph in MATLAB. The points are (x,y,z). I would like to have a SCATTER plot on the (x,y) axes. But then each one of these (x,y) points are LINE connected to their respective z point. If anyone has code for this, or know how to do this in SAS...
I would like to use Mathematica Integrate function. But how do I specify the following interval
(0 , Pi/2 ]
When I write
L \[Element] (0, Pi/2]
It simply bolds ( and ] in orange in error.
How do I get Mathematica to recognize that for the integrand, my value L is...
Yes, I looked at that more closely and realized that is wrong. The question behind the question is, what is the rate of the following at which the function below approaches zero:
lim (1/y) arccot [ -exp(x)/sin(y) - cot(y) ] ->0 as x->infinity
where y is (-pi,0)
Yes, it does.
What if my f(x) = e^x + cot y ... where my y is another variable for which cot y may diverge to positive infinity? I am still only interested in the rate for when x -> infinity.
What would g(x) look like for the rate at which the new f(x) approaches infinity at the same...
The actual functional analysis for my rate of convergence is a bit more complicated. But essentially the problem I have is knowing if the following is true:
lim exp(x) -> infinity as x->infinity
is at the same rate as
lim exp(-x) -> 0 as x-> infinity
? Would really appreciate...
Perhaps this may be correct...
1. arcot = ( pi/2 - arctan() )
2. lim 1/d * [ pi/2 - arctan() ] as x->infin
3. We know that the express above goes to zero. We just want to know how fast. So
lim 1/d * [ pi/2 - arctan() ] = 0 as x->infin
4. 1/d * arctan[ - exp(cx) / sin(d) ]...
Hmm... perhaps a rephrase of the question is more appropriate.
I want to take the limit of the following function as x -> infinity
(1/d) * arcot [ - exp(cx) / sin(d) ]
where d is (-pi,0)
Now a prior condition would stipulate that the above has to go to zero as x tends to infinity...
So if my function was
LN [ -exp(cx)/sin(d) - i ] = ?
Then, I would decompose it to real and imaginary parts?
The larger problem is
LN [ -exp(cx)/sin(d) - i ] - LN [ -exp(cx)/sin(d) + i ]
where c and d are constants.
I am using MS Visual Studio as the compiler. I have a c++ routine that I needed in my current project, which I saved under my Header Files. This file is needed for the compiler to interpret certain variable declarations. However, when I F7 to compile I get the following error...