All Questions
Tagged with calculus-and-analysis functions
270 questions
0
votes
2
answers
63
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Derivative of unknown function with respect to global defined function
I have the following code:
x[t_]:=y[t]+2*t
MyRule = D[z[x[t]],x[t]]>0
y[t] and z[x[t]] are unknown functions.
I get the following error message: "D: 2t+y[...
- 1
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 ...
- 101
0
votes
0
answers
99
views
How to know the formula of function in mathematica?
When I review BiorthogonalSplineWavelet in official website.
I could not find any formula of how to calculate as below:
How to ...
- 707
2
votes
3
answers
236
views
Trouble with branch cuts plotting a real function
When I plot the following function
...
0
votes
1
answer
61
views
Computing an exact range with FunctionRange
When using FunctionRange to compute the range of the two-argument ArcTan function, Mathematica fails to return an exact answer.
...
- 536
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 ${}_2F_1$:
\...
- 139
1
vote
2
answers
131
views
Issue with variable within Sum[] bounds
I have the following sum that starts from a variable lower bound index $n$:
$$\sum _{y=n}^x \frac{n^2! \left(n^2\right)^{-x} \mathcal{S}_x^{(y)}}{\left(n^2-y\right)!}$$
I tried to compute a closed ...
- 197
0
votes
1
answer
30
views
0
votes
1
answer
111
views
Simplifying an ODE in Bessel notation
I have the following Mathematica code:
eq[r_] = 3 (1 + 2 a) g1 r y[r] - 2 (2 y'[r] + r y''[r]);
DSolveValue[eq[r] == 0, y[r], r]
This gives me the ...
- 2,963
1
vote
2
answers
76
views
Why is the result of this integration coming out as a list if the function being integrated just returns a numerical value?
I am trying to integrate over a Dirichlet distribution. Instead of using the built-in function, I defined it myself as:
...
- 11
0
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0
answers
44
views
0
votes
0
answers
50
views
Function returning error every other run
Disclaimer: I am new to Mathematica but have some experience with other programming languages.
I have defined the following function (simplified version):
...
- 1
1
vote
1
answer
47
views
Issue with FullSimplify in StirlingS2 definition
I have previously asked a question about a problem simplifying an expression in Mathematica. The solution was to expand the definition of StirlingS2.
This time, I ...
- 197
0
votes
1
answer
49
views
Problem calculating mean of probability distribution
I have a discrete probability distribution where $P(X=x)=(Factorial[n]/(n^x))*StirlingS2[x-1,n-1]$. So, when trying to calculate its mean with the following property: $\mu = \sum_{i} x_i \cdot P(x_i)$,...
- 197
1
vote
0
answers
75
views
How can I ask Mathematica to give the explicit real form of the given function?
In part of my calculations, I obtain this expression which contains the imaginary unit I but I expect that this expression might be real (from the comments below, ...
- 195
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:
...
- 420
0
votes
1
answer
135
views
Is it possible to get rid of `Root` and have an explicit closed-form solution for the given equation?
I want to solve the given equation for m>0 where all parameters are Reals and a<0. ...
- 63
1
vote
2
answers
151
views
Is there any hope that Mathematica answers this parametric integral? [closed]
Is there any hope that Mathematica answers this integral?
Integrate[ Exp[a (b/(c + 2 (1 + x) d)^4 - (e + f/(c + 2 (1 + x) d)^2)^2/(
4 (2 + x + g)^2))], x]
...
- 749
1
vote
1
answer
89
views
Recursive application of Grad in scalars
I am looking for an efficient way to apply Grad recursively to a scalar function. The code I have so far is in the structure below. I define the scalar function outside the loop, take its derivatives ...
- 719
5
votes
3
answers
584
views
Finding Saddle Points [closed]
How many saddle points are on the graph of $h(x,y)=x^3-12xy+8y^3?$
I need to find the critical point of this function, but I get stuck when I have to find the partial derivatives of fx and fy.
How can ...
- 51
0
votes
1
answer
124
views
Riemann surface of the argument multivalued function
I tried to use Michael Trott's Mathematica Resource function RiemannSurfacePlot3D for plotting the Riemann surface of the Arg function without success. How can I plot this Riemann function with the ...
- 141
2
votes
2
answers
258
views
Taking the derivative of Re[f]
I have looked at similar posts, such as this one, but none of the solutions have worked for me. I have an imaginary function, and I have tried to obtain its real part using ...
- 21
5
votes
0
answers
134
views
Create custom definition for chain rule of partial derivative of a vector-valued function
I'm trying to calculate derivatives of expressions involving an unknown function $F: \mathbb{R}\times\mathbb{R}^n\times\mathbb{R}^n \rightarrow \mathbb{R}^n$, with respect to a parameter $h \in \...
- 191
1
vote
2
answers
277
views
How to interpolate an implicit function?
chi(t) is implicit function. The implicit function can be plotted by ContourPlot.
Is it possible to obtain chi(t) explicitly using function interpolation?
...
- 1,893
1
vote
2
answers
156
views
How to calculate the depth of the lake in mathematica?
I want to calculate mean depth of Goose lake (mean depth=4.6 m), I use bellow command for this operation, But this command is not automatic and we have to create the coordinates manually, and on the ...
- 195
3
votes
0
answers
136
views
How to estimate Lake area and volume in Mathematica?
I have a satellite image of the lake and I want to estimate its area and volume.
Actual volume:1.49*10e8 m^3
Actual Area:36.9 km^2
I did the following command to find the volume, but it is not very ...
- 195
1
vote
2
answers
188
views
How to do edge detection in Mathematica?
I have some pictures of water level and I want to do edge detection, I used the following command, but this command is vertical edge detection and I want horizontal edge detection and water level. ...
- 195
0
votes
1
answer
83
views
How to make a density plot for an isotropic function written in cylindrical coordinates?
$f(\rho,z)=2\rho^2+\frac{2}{3}z^2 \quad$ is a function in the cylindrical coordinate system $(\rho,\theta,z)$
The function $f(\rho,z)$ is isotropic because it does not depend on the angle $\theta$. ...
- 1,893
2
votes
1
answer
104
views
How can I let Mathematica know that the Laplacian of a function is zero?
Suppose I have a long algebraic expression, and in there somewhere I have derivatives of a function V[x,y,z].
I want to set
...
2
votes
2
answers
180
views
How to make delayed function evaluate to zero
I have a function
y[r_] := D[otherfunction[r],t] + D[r,t];
where $r$ can pick up a time dependence depending on the problem. When it does not I am having issues ...
- 23
2
votes
3
answers
181
views
How to write a function in the following form f[a_, b_, c_,...] so that it is flexible with respect to the number of arguments?
@lericr have written under several of my questions that the way I try to modernize the code could be made much simpler. Below is the original part of the code. The remaining parts have similar designs,...
- 1,893
2
votes
1
answer
89
views
How to correctly reassign variables {c11 -> p11, c12 -> p12} using a Table or some other similar structure?
Why is the value of the function Pxx[1,2] is a number but the function Pxxx[1,2] is an expression? Isn't this construction ...
- 1,893
0
votes
1
answer
185
views
Plugging in a value after taking partial derivative [closed]
I am trying to write a code where I have a function of two variables, take the partial derivative with respect to each variable and finally plugs in specific values for the variables. To be more ...
- 49
2
votes
2
answers
112
views
How to use sequence of variables (Sequence) correctly?
Why does the function EER[1,2] have a different value than the function EERR[1,2]? Isn't the entry ...
- 1,893
1
vote
2
answers
71
views
Why does Mathematica not see some of the function PxB1[a10_, b10_, qa0_, qb0_, c11_, c12_] variables?
Why does Mathematica not see the c11 and c12 variables in the function PxB1[a10_, b10_, qa0_, qb0_, c11_, c12_]? How to fix it?
...
- 1,893
2
votes
2
answers
77
views
The correct notation of a function that contains an expression with NIntegrate
I tried to set the function Px[a1_, b1_, qa_, qb_]. Why does Px[1.22, 0.44, 1.40, 1.81] not give out a specific number?
...
- 1,893
0
votes
1
answer
34
views
Is it possible to ask Mathematica to order this expression in terms of descending absolute values of the arguments of the exponential functions?
I have the given expression which is a sum of exponential functions with some parameters $a,t,u,y$ where $a>0$.
Question
Is it possible to ask Mathematica to order this expression in terms of ...
- 349
1
vote
2
answers
58
views
Integrate function [closed]
I want to find the constant in front of the term of the integral that only contains $x$ in the following function:
$$f(x) = \frac{(56-15 \sin x + \sin^2 x)^2}{6-5 \sin x + \sin^2 x}$$
This is my input ...
- 27
3
votes
2
answers
167
views
Optimizing execution time and exploring closed form solutions in Mathematica's DSolve
I am encountering two issues while running the following code in Mathematica:
Slow execution: I have been running the code for approximately 30 minutes, but it is still executing. I am using Windows ...
- 873
0
votes
1
answer
63
views
How to properly expand a list with certain numerical elements?
There is a list with 19 elements ...
- 1,893
0
votes
1
answer
150
views
How to expand the existing basis set so that it becomes more complete?
I have a set of anisotropic gaussian basis set which describes the ground state of the system with great accuracy.
The Hamiltonian of the system has the following form: $$H=-\frac{1}{2}\Delta-\frac{1}{...
- 1,893
3
votes
3
answers
145
views
2
votes
3
answers
232
views
Slope-demarcated PlotStyle implementation
In the above graph, I would like to display plots with slope-dependent plot styles (solid, dashed and dotted).
Specifically, the regions a---b1, a---b2 and a---b3 with solid lines(...
- 2,730
2
votes
1
answer
83
views
Why does Series give two different results for given function?
I want to do Series of this function x^12 Cos[y x]^2 Sin[y x]^6 Sin[(-1 + Sqrt[3]) y x]^2 around ...
- 349
0
votes
1
answer
125
views
Can Mathematica estimate this complex function?
Mathematica has given me a function in $x,r$ given by
...
- 35
3
votes
2
answers
165
views
Recursive function with subscript
I am trying to define a recursive function with a subscript. Something similar would be $f_{n+1}(x) = \int 3 x f_{n}(x)dx$. I've tried lists, For function, ...
2
votes
2
answers
274
views
How can I find the nature of a turning point?
I have this function which has 4 turning points:
$$f(x)=18m^4 x+42m^3 x^2-54m^2 x^3-42 m x^4+36x^5$$
f(x)==18m^4 x+42m^3 x^2-54m^2 x^3-42 m x^4+36x^5
However, I can'...
- 21
1
vote
1
answer
60
views
Value given by NIntegrate is double of Integrate function
I am performing a calculation where the result of NIntegrate and Integrate is different. They differ by factor of 2. Can someone tell what is the reason and how to make the NIntegrate value right?,
<...
- 194
2
votes
2
answers
150
views
Is it possible to ask Mathematica to find those points $(x,y)$ at which the given function may reach its global/local extrema?
I have this two-variable function $f(x,y)$ for {x,-Pi,Pi} and {y,-Pi,Pi} in which $\{a,b,c\}$ are real parameters (can be ...
- 195