Questions related to the calculus and analysis branches of Mathematica, including, but not limited to, limits, derivatives, integrals, series, and residues.

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3answers
252 views

Solving an Integral Numerically

I have been trying to solve the integral equation below, but cant seem to find a way out of this. Can someone please help me out with suggestion? $f(t)=\int_0^{\infty}\frac{K_1a(t)}{a(t)+K_2}\,dt$ ...
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2answers
664 views

About generating power series

For an arbitrary function $f(x,y)$ I am defining functions LogMT1 and LogMT2 as follows, ...
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1answer
40 views

Expanding derivatives of hypergeometric functions

Sometimes Mathematica expresses results of integration or summation in terms of symbolic derivatives of Hypergeometric2F1 function, and cannot further simplify ...
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1answer
41 views

Finding a root of a parameterized integral

I have a function given as a parameterized definite integral: f[a_] := Integrate[BesselJ[0, x - a] BesselJ[0, x + a], {x, -∞, ∞}] I suspect it has a root near ...
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1answer
60 views

Integrate and NIntegrate yield different results for double integral

Evaluating a double integral with bivariate normal distribution yileds widely different results depending on the method used. I define a bivariate normal distribution with {10, 3} and {8, 1.5} as ...
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1answer
46 views

Integration of linked PDFs over probability simplex

I'm trying to integrate the following expression: f[a1,p1+p2+p3+p4]*f[a2,p2+p3+p4]*f[a3,p3+p4]*f[a4,p4] Where ...
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0answers
66 views

Algebraic condition from a non linear equation

I have got a system of equations which look like this: $\theta_{1}^{2}e^{\phi_{1}\cos(\Omega z)}\tilde{w}\cos^{2}(\theta_{1}\sin\Omega z)\sin^{2}\Omega z+\frac{1-\lambda\cos(2\theta_{1}\sin\Omega ...
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0answers
51 views

Reducing a long complex expression to a simplier one by using assumptions

so I have an ugly looking equation that I wish to solve under some specific circumstances. Using DSolve I write; ...
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0answers
142 views
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0answers
120 views

Approximating a stochastic integral with a Wiener process

I would like some assistance to solve the following: $\sum\limits_{i=0}^{n-1} e^{-k(n\Delta t -i\Delta t)}\Delta z_i$ where $z$ is a Wiener process, $\Delta z_i = z((i+1)\Delta t)-z(i\Delta t)$. ...
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0answers
96 views

Non-Solvable PDE?

I would like to know whether this PDE is solvable and if yes, for which values of $a$. ...