Questions on the special mathematical functions implemented in Mathematica.

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0
votes
1answer
36 views

Plotting a function based on complicated integral

I have this function : f[Lambda_] := K Integrate[x Exp[- x^2-Lambda x] HypergeometricU[-Lambda,1/2,(x+ Lambda/2+2)^2],{x,0,Infinity}]; where ...
3
votes
1answer
38 views

Interval arithmetic for DawsonF (or other special functions)

I am currently trying to estimate a complicated expression involving DawsonF using interval arithmetic. The interval arithmetic is partially supported by ...
0
votes
0answers
50 views

Solving Fredholm equation of the 2nd kind

While I was using the code from here to solve this integral equation: ...
0
votes
1answer
56 views

$\tt DiracDelta$ behaves incorrectly on multidimensional integral [duplicate]

Is there a reason why this seems to work: Integrate[DiracDelta[x] F[x], {x, -Infinity, Infinity}] F[0] But this does not: ...
7
votes
2answers
114 views

Portion of Curve Omitted by Plot

In the course of addressing question 104559, I encountered the following problem with Plot. Begin with ...
5
votes
2answers
146 views
1
vote
1answer
92 views

Use Meijer-G function to represent elementary functions

I want to represent these elementary functions: $x^{2}\sqrt{x}$, $\sin{4x}$, and $x\ln{x}$ as cases of MeijerG. What arguments should I give to ...
6
votes
3answers
242 views

Labeling solutions of an Eigenvalue equation involving Bessel functions

I'm solving the Schrödinger equation for a particle in an annular geometry with hard wall boundary conditions and I've reduced it to the following equation: $$J_m(k\,R_1)\,Y_m(k\,R_2) - ...
5
votes
2answers
147 views

Symbolic integration of SphericalBesselJ

Backslide introduced in v10 and persisting through v10.3.1. Consider the following integral ...
8
votes
0answers
68 views

$\tt SphericalHarmonicY$ does not seem to be an eigenfunction of the spherical harmonic equation

I applied the spherical harmonic equation on the SphericalHarmonicY functions like this: ...
4
votes
1answer
54 views

convert MeijerG to form Standard Functions in Mathematica

I'd like to convert MeijerG[{{}, {1., 1.}}, {{0., 0., 4.}, {}}, -1. T λ] to its Standard Functions (For example Bessel function or ...). Any suggestion?
1
vote
1answer
75 views

How to make this code involving Hypergeometric functions to run faster?

This question is followed up from this Question. I would like to thank Dr. Hintze and I_Mariusz for the comments and help. I am pretty new to mathematica ( I just learned it 4 days ago) so I would ...
5
votes
2answers
282 views

Inverse Laplace transform

Let $r=\mu = 0.15; \sigma = 0.05; T = 1; S_0 = 100; K = 95;$ Let $\nu:=\frac{2\mu}{\sigma^2}-1$ and $\eta \equiv\eta(\alpha):=-\frac{\nu}{2}+\frac{1}{2}\sqrt{\nu^2+\frac{8\alpha}{\sigma^2}}$. ...
1
vote
1answer
65 views

Integrating sinc function over discontinuity

I would like to analytically integrate the sinc function. First of all, if I just perform the integration the following way, everything is as expected: ...
3
votes
1answer
58 views

Convert an expression to use a specific analytic form

I have an expression that evaluates to an expression containing multiple ExpIntegralEi expressions. However, I would prefer that Mathematica use ...
2
votes
1answer
51 views
3
votes
2answers
82 views

Show Factorial instead of Gamma in the result of RSolve

Now I wanted to solve for a recurring function with RSolve. Here's how I tried: ...
1
vote
0answers
74 views

How to understand the symbolic integral in a result returned by DSolve?

I am trying to solve an ODE like $$\frac{dF}{dx}=\frac{a}{\ln^3 x+[c+d(ax+b)][2\ln x+c+d(ax+b)]\ln x},$$ where $a,b,c,d$ are constants. I guess it could contain a special function, say, the ...
0
votes
1answer
71 views

Implementing AiryAiPrimeZero function

There are some functions implemented in the Wolfram Language related to Airy functions. For example, AiryAi, AiryAiZero or ...
3
votes
1answer
79 views

Question about PrimeZetaP

The PrimeZetaP function appears to give results for complex s with real part > 0. Apparently, the analytic continuation is built ...
0
votes
3answers
117 views

Find zeros of function in 2 variables

I have two functions $f(r,\phi)$, and $g(r,\phi)$. What is the best way to find the curve in the plane $(x,y)$ or $(r,\phi)$, over which $f(r,\phi)=g(r,\phi)$? I know how to plot it, using ...
7
votes
2answers
149 views

Derivative of the Dedekind eta function fails to compute with errors I don't understand

When trying to understand better the question Eisenstein Series in Mathematica? I stumbled on the following: issuing Derivative[1][DedekindEta][.11 I] gives ...
4
votes
1answer
224 views

Find solution of nonlinear ODE in terms of JacobiCN

I am trying to find a specific solution for this differential equation: $-\frac{1}{2}\frac{d^2}{dx^2}\psi(x)-2k \; \psi(x)^3 + \frac{1}{2}k^2\; \psi(x)=0$ MMA gives me a solution in the form of a ...
1
vote
1answer
50 views

Integrating the product of two imaginary error functions

I am trying to evaluate the following integral: Integrate[Erfi[y] Erfi[z + y] , {y, -L, L}] which simply returns the input. How could I force ...
1
vote
0answers
39 views

Problem on special functions

What does the symbol PolyLog^{(0,1)}(0,1/e) mean? I know the meaning of the Polylogarithm, but what is that exponent? It happens the same with the Lerch zeta function!! Thanks in advance.
2
votes
2answers
56 views

How to solve or plot roots of the equation involves Bessel function of first and second kind?

Here is my equation x^2 + BesselJ[m,k*x^2]*x + k*BesselK[m,k]==0. I would like to solve this equation for different initial guesses of ...
2
votes
1answer
89 views

making 3d listplot smoother? [closed]

This is a continuation of my previous two questions: this one and this one. I would like to plot the following function $$ p(x,t) = \frac{e^{-1/A}}{A}\sum_{i=1}^{500}e^{c_i\, t}m_i(x)\frac{z_i}{w_i}, ...
7
votes
1answer
146 views

How can I get the solutions of $x^n-x-t=0$ in hypergeometric form?

$x^3-x-t=0$ has three roots that can be expressed in hypergeometric form $$x_1=-1-\frac{t}{2}{_2F_1\left(\frac{1}{3},\frac{2}{3};\frac{3}{2};\frac{27t^2}{4} \right)}+\frac{3t^2}{8} ...
7
votes
2answers
189 views

Confusion regarding the incomplete elliptic integral of the first kind

I am trying to manipulate a conformal map from the half-plane to a square $z \rightarrow w(z)$ defined by: $$ w(z) = \int \limits^{z} dx \frac{1}{\sqrt{(1-x^2)x}} = \sqrt{2} \; ...
5
votes
1answer
179 views

Precompiling a Whittaker function

Is there a way to speed up the evaluation of special functions in Mathematica? I am particularly interested in the Whittaker W function. For instance, the following piece of code: ...
1
vote
2answers
46 views

Calculating the numerical value of the regularized generalized hypergeometric function

I'm trying to calculate the numerical value of the regularized generalized hypergeometric functions: $\qquad \sf{HypergeometricPFQRegularized}^{(\{1\},\{0,0\},0)}(\{-1.5\},\{-1.,-0.5\},3600.)$ I ...
6
votes
2answers
271 views

How to implement a numerically efficient Airy Zeta Function

Define the Airy zeta function for $n=2,3,\dots$, by $$ Z(n) := \sum_r \frac{1}{r^n}. $$ where the sum is over the zeros $r$ of the Airy function $\operatorname{Ai}$. In Mathematica the ...
0
votes
1answer
70 views

Can I tell DSolve to solve a first-order ODE by method of separation of variables?

I meet a first-order ODE $$\frac{dy}{dt}=\frac{a(\ln\frac{1-c}{1-y})^3}{\frac{b-y}{1-y}+\ln\frac{1-c}{1-y}},$$ where $a,b,c$ are constants. The ODE is subjected to the initial condition $y(t=0)=y_0$. ...
0
votes
1answer
65 views

Plotting complicated Bessel functions expression

I am trying to plot this function ...
3
votes
2answers
335 views

Solve stiff system by shooting method

I'm trying to solve a second order differential equation with the shooting method but, it appears to be a stiff system. This is worst for a larger parameter $\mu$. I've tried different methods: ...
4
votes
0answers
114 views

Puzzled by Assumptions [duplicate]

I don't know if this has already been discussed. Integrate[BesselJ[2 m + 1, x], {x, 0, ∞}, Assumptions -> m ϵ Integers] ...
4
votes
1answer
146 views

Bad performance of Integrate (and WolframAlpha) for an Integral of Bessel function of the first kind

The following returns unevaluated in WolframAlpha. Also in my machine Mathematica needs quite a lot of time to compute it. ...
2
votes
1answer
65 views

FullSimplify gives wrong answer when operating on HypergeometricPFQ

When I try to simplify this hypergeometric function FullSimplify[HypergeometricPFQ[{1/2 - n/2}, {-(1/2) - n/2}, -a^2]] Mathematica 10.0.1.0 returns ...
1
vote
1answer
77 views

Plot Meijer G function [closed]

How to plot using Mathematica the Meijer G function $$ G^{m l}_{p q} \left(\omega t \ \Bigg\vert \ {a_1,\cdots,a_p\atop b_1,\cdots,b_q} \right) $$ Thanks
2
votes
1answer
85 views

How can I plot the normalized distribution of the Riemann zeta zeros?

Given a list of eigenvalues or a list of Riemann zeta zeros, how can I plot this famous plot found here: On the page referred to, You need to click on "Programs", "The Riemann zeta function" and ...
1
vote
1answer
46 views

Failure of Series[] for hypergeometric functions

I am encountering peculiar errors when asking Mathematica for series expansions of certain hypergeometric functions. To give an example, consider the function $f(x) = {}_{5} F_{4}(3/2,3/2,3/2,2,2; ...
2
votes
2answers
69 views

Integration result with incomplete beta function

I'm doing some calculations (double integration) which results in the incomplete beta function occurring as an end result. My input is: ...
5
votes
2answers
70 views

Solution to Simultaneous Arithmetic/Geometric Mean Recursion Relations

I'm trying to solve the simultaneous convergent sequences of geometric/arithmetic means where $a_{n+1}=\frac{1}{2}(a_n+b_n)$ and $b_{n+1}=\sqrt{a_nb_n}$ and initial values are $a_0=1+x$ and $b_0=1-x$. ...
1
vote
1answer
86 views

Can anyone re-produce this result related to the spectrum of Riemann Zeta using error term generated from MangoldtLambda?

All: I tried to reproduce the results from this page: How to plot the Riemann-Zeta zero spectrum The following is the code that was posted on above page: ...
0
votes
1answer
42 views

Plotting precise intersections involving singular functions

I have pseudo-elliptic functions defined on a parallelogram within $\mathbb{C}$ and I would like to clearly highlight the path within this parallelogram which satisfies the real part of my ...
0
votes
0answers
33 views

Determine class of special function from algebraic constraints?

Consider vectors x_i in arbitrary dimension. Let's say I have an expression in six variables F[x_1,x_2,x_3][x_4,x_5,x_6], which ...
1
vote
0answers
58 views

Why can't I use OmegaPrime to find the Limit of Prime[n]? [duplicate]

I've looked at these links already; What are the limits of the Prime-functions? What is so special about Prime? which gave an answer for earlier versions of Mathematica. Yet when I try to input ...
0
votes
1answer
114 views

How to plot zeros of confluent hypergeometric function

I am fairly new to mathematica so I need a little bit of help. I need to plot the zeros of an equation containing confluent hypergeometric functions. The equation i need to solve is given by the ...
2
votes
3answers
375 views

Solve an equation that include Gamma

I want to solve the following equation Solve[Gamma[1 + x]/Gamma[x - 1/2] + 1 == 0, x] I have answer x=-0.25, but I can not obtain this answer with Mathematica. ...
2
votes
1answer
99 views

Plotting a partial sum

I am given the Legendre expansion of the first kind. $$f(x)=\sum_{n=0}^{\infty}A_{n}P_{n}(x).$$ I have worked the coefficient to be $$A_{n}=\frac{1}{\left \| P_{n}(x) \right \|^{2}} ...