Questions on the special mathematical functions implemented in Mathematica.

learn more… | top users | synonyms

0
votes
1answer
72 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
78 views

Plotting complicated Bessel functions expression

I am trying to plot this function ...
3
votes
2answers
416 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
117 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
170 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
85 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
124 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
3
votes
1answer
137 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
55 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; 1,...
2
votes
2answers
84 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
83 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
91 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
44 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 pseudo-...
0
votes
0answers
39 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
59 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
123 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
421 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
118 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}} \int_{x=-1}^{x=1}...
5
votes
2answers
99 views

Expanding PolyGamma function error

Bug introduced in 6.0 or earlier and fixed in 10.3.0 For large half-integer arguments of the PolyGamma[] function, ...
1
vote
0answers
84 views

Legendre expansion of functions [closed]

I am given the expansion for the Legendre function of the first kind. It is just $$f(x)=\sum_{n=0}^{\infty}A_{n}P_{n}(x).$$ I have found the expression for the coefficient $A_{n}$. However I would ...
3
votes
1answer
108 views

Range of summation in simple Plot seems off

I was trying to reproduce a picture in a book by Havil of the sum, $$s = \sum_{r=1}^{\infty}\frac{\mu(r)}{r}\left(Li(x^{\rho_k/r})+Li(x^{\rho_k*/r})\right) $$ using ...
3
votes
0answers
80 views

Refining a density plot of the Eisenstein series argument [closed]

Thanks to amazing code from "Guess who it is" here: Eisenstein Series in Mathematica? I'm able to make some nice plots using Eisenstein Series. What I'd like is a color plot of the argument of certain ...
1
vote
0answers
74 views

Odd plotting/math issue (could be a precision problem) [closed]

I've got a pretty odd error on a project I'm working on and was hoping to enlist some advice to fix it. The goal of this notebook is to show that I can eliminate the non-normalizable (blowing up part) ...
4
votes
4answers
267 views

How to stop a summation when a variable is small enough?

I meet with a problem. I hope to get an infinite summation of $f1(x)/f2(x)$ which converges to zero. So my code is Sum[f1[x]/f2[x],{x,Infinity}] or ...
1
vote
1answer
49 views

problem about Root and Hypergeometric2F1

See these example, why does the output is different? ...
2
votes
0answers
97 views

Nasty integral advice

I have a pretty ferocious integral to solve, and since it doesn't seem I'll be able to do much analytically, I've taken to Mathematica to get some information. Mainly, I want to see if there are any ...
6
votes
2answers
144 views

Plot of The RiemannSiegelZ Function

I would appreciate your help to visualize the of the following function RiemannSiegelZ[x] with this range. { 18154980120849865 , 18154980120849885 } I tried this: ...
0
votes
1answer
56 views

Sum of hypergeometric functions, variable number of arguments

How can I write in Mathematica an expression like this? $$\sum_{k=1}^n {_{k}F_{k}} (1,1,\dots,1; \,2,2,\dots,2; \,z) ~,$$ where ${_{p}F_{q}}$ is the generalized hypergeometric function. My problem ...
1
vote
0answers
58 views
0
votes
0answers
44 views

Timing of associated Legendre polynomials

I encountered a strange issue with the associated Legendre polynomials implemented with LegendreP[l,m,z]. Quite simply, the time used for the numerical computation of those quantities depends on ...
6
votes
2answers
192 views

How does Mathematica calculate LaguerreL

About the function LaguerreL[n,a,x], the helping documents in Mathematica only say that this function satisfies equation $xy^{\prime\prime}+(a+1-x)y^\prime+ny=0$. ...
4
votes
1answer
95 views
6
votes
1answer
107 views

Spurious infinite limit of integration message in NIntegrate

Bug introduced in 7.0 and persisting through 10.2 NIntegrate returns an error complaining that ComplexInfinity is an invalid ...
12
votes
1answer
340 views

Eisenstein Series in Mathematica?

Mathematica doesn't seem to have built-in tools to deal with the Eisenstein series: $$\begin{align*} E_{2}(\tau)&= 1-24 \sum_{n=1}^{\infty} \frac{n e^{2 \pi i n \tau}}{1-e^{2 \pi i n \tau}}\\ E_{...
1
vote
0answers
72 views

Use Solve[] with Bessel, gamma, and hypergeometric functions?

I need to find values of {a,b,c} such that the 0th, 2nd, and 4th order moments of f[x]=Exp[-ax^4 - bx^2 - c] will equal respectively {1,2,10}. I didn't really expect this to work, and it didn't: <...
3
votes
2answers
232 views

Storing Variables in “Loops” and Point Plotting

Given the function $y=\sin x$ defined over the region $-\pi \leq x \leq \pi$, I need to implement a "do loop" such that I sweep over 100 or so points $-1 \leq y \leq 1$ and find precisely the two $x$ ...
-1
votes
1answer
199 views

Inverse of a Digamma/ Polygamma Function

How one can find the inverse of a digamma/ Polygamma function in Mathematica 10?
7
votes
2answers
120 views

Simplify expression to Integer

I have the following function: f[n_]:=(n-1) E Gamma[n,1]; I know that this expression always evaluates to an Integer, but Mathematica doesn't always output the ...
2
votes
1answer
134 views

Unexpected Weierstrass $\wp$-Function Behavior

In Mathematica, the Weierstrass $\wp$-function is expressed by WeierstrassP[u + I v, {g₂, g₃}] where g₂ and ...
0
votes
1answer
95 views

Why is the indefinite integral $e^\frac{x}{2}x^\frac{g}{2}dx$ the upper Gamma function in Mathematica? [closed]

I have an indefinite integral $e^\frac{x}{2}x^\frac{g}{2}dx$, I try to solve in Mathematica. Solve[Int[e^{x/2}x^{g/2-1}dx ,x]] (* Gamma[g/2,x/2] *) How does ...
3
votes
2answers
176 views

ParametricPlot with 2 variables

I want to try plotting this: As you can see the first axis is v and the second is just dependent of the angle of $\Phi$ . The function is ...
1
vote
0answers
88 views

Improve speed of evaluating a sum over four indices

I am trying to implement the Fox-H function with several variables as sum of residues. I have arrived at the following function; ...
3
votes
2answers
379 views

How I can integrate $\int_0^{a} x e^{-\frac{b^2 x^2}{2 c}} J_0(n x) dx$?

How can I get a solution to the integral given below ? $\quad \quad \int_0^{a} x e^{-\frac{b^2 x^2}{2 c}} J_0(n x) dx$ where $a,\,b,\,c$ and $n$ are constants and $J_0$ is a Bessel function of the ...
3
votes
3answers
183 views

Calculating $\lim_{x\to 1} \, \int -\frac{i \text{Li}_2\left(x-x^2\right)}{\sqrt{3} \left(x-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)} \, dx$

How can we force Mathematica to compute this limit? $$\lim_{x\to 1} \, \int -\frac{i \text{Li}_2\left(x-x^2\right)}{\sqrt{3} \left(x-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)} \, dx$$ It seems it ...
5
votes
2answers
253 views

Evaluating a Series expansion of PolyLog function

I am trying to evaluate an expansion of the following integral $$ \int_0^\infty \frac{p^4}{1+\exp\left({\frac{p^2}{2mT} - \frac{\mu}{T}}\right)}\, dp = A_0(m,\mu) + A_2(m,\mu)T^2 + \ldots $$ in terms ...
1
vote
3answers
253 views

Find all roots of a function with parabolic cylinder functions in a range of the variable

I want to find all roots of a function involving Parabolic Cylinder Functions. In what follows, I define 2 variables $\xi1$ and $\xi2$, which in turn depend on $\omega$. My function is then defined as ...
7
votes
2answers
144 views

Generating terms of the Stirling series

The Stirling series starts as follows: $$n!=\left(\frac{n}{e}\right)^{n}\sqrt{2\pi n} \left\{1+\frac{1}{12n}+\frac{1}{288n^{2}}-\frac{139}{51840 n^{3}}-\frac{571}{2888380 n^{4}}+O\left(n^{-5}\right)\...
3
votes
0answers
84 views

speed up evaluating a listable function [duplicate]

I apologize in advance for the vagueness, but I can't think of a more descriptive title. I am trying to find the average value of the square of BesselJ[0, x] ...
15
votes
4answers
618 views

How to plot Ramanujan's continued fraction in Mathematica?

I want to plot Ramanujan's continued fraction: $$R(q)=\cfrac{q^{1/5}}{1+\cfrac{q}{1+\cfrac{q^2}{1+\ddots}}}$$ but I do not know how to define this function in Mathematica. How do I define and plot $R(...