All Questions
9 questions
0
votes
3
answers
126
views
How to compute the Jacobian matrix using Mathematica [duplicate]
Apologies if this is posted to the wrong forum. Have been using Maple and Maxima for 20+ years, and have only recently started using Mathematica (v. 14). Having a heck of a time getting Mathematica to ...
- 59.6k
5
votes
0
answers
171
views
Hypergeometric Function Integration Using Mellin-Barnes Representation
I have the following integral:
$$
I=\int_0^1 d \alpha d \beta d \gamma r(\gamma) s(\alpha, \beta) T(\alpha, \beta, \gamma)
$$
where I define
$$r(\gamma)=(\gamma(1-\gamma))^{ -1 / 2+\epsilon / 2}$$
and,...
- 139
1
vote
1
answer
198
views
Integration and expansion of hypergeometric function
I am trying to reproduce the evaluation of the expansion in $\epsilon$ for the function in Appendix B of the paper arxiv.org/abs/0705.0676v3, which involves the hypergeometric function ${}_2F_1$:
\...
- 16.6k
1
vote
0
answers
104
views
Differentiation of Parabolic Cylinder Functions and Hermite Polynomials w.r.t to Order
When I evaluated (ver. 12.3) parabolic functions below in the vanishing order limit: $u \rightarrow 0$, I got the following:
...
- 29.1k
7
votes
1
answer
308
views
How to use Slater Type Orbitals as a basis functions in matrix method correctly?
This question is a continuation of my previous series of questions about basis functions.
I would like to find the minimum energy of Coulomb potential motion using matrix method.
$H=-\frac{1}{2}\Delta-...
- 50k
7
votes
1
answer
256
views
Keeping Phase Factors in Sqrt
I am trying to plot certain holomorphic functions that contain square and higher roots. In the complex analysis sense, the function $f:z\mapsto z^\alpha$ for some $\alpha\in\mathbb C$ has a phase ...
- 2,914
1
vote
2
answers
266
views
Why can't Mathematica evaluate this integral?
I want to work with the rectangle function, which I define by
f[x_, m_] := Limit[1/((2*(x - m))^(2*k) + 1), k -> Infinity];
(I know that in theory I can use <...
- 17.4k
3
votes
2
answers
903
views
Nested Integrate and NIntegrate: Analytic and Numeric solutions?
Here is a function $F(r)$ which contains double integrations
$$F(r)=\exp\left[ \int_{0}^r dw \,\exp\left(-\int_{0}^w ds
\frac{s^2}{s^2+1} \left(1-\exp(- s)\right) \right) \right]$$
I am fine ...
- 431
0
votes
1
answer
262
views
Finding the limit of the following functions involving the Bessel function of the first kind
I want to find the value of the functions $f[x,y,\theta]$ and $g[x,y,\theta]$ involving the Bessel function of the first kind, a Gaussian and a linear/algebraic function in the limit $\theta\...
- 273k