810 views

### Numerical instability in cosh and sinh - integral functions [duplicate]

I'm trying to calculate the function: CoshIntegral[x] Sinh[x] - Cosh[x] SinhIntegral[x] Unfortunately Mathematica seems to hit a point (x~20) and things become ...
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3k views

### A problem about function N

Toady,I have a problem about N,described as below: For example N[1/3, 5] (* ==> 0.33333*) and ...
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### Very different results from evaluating same expression with different precisions

When I evalute the following expression, ...
• 749
401 views

### Plot of $\sin(x^x)$ is missing from $x=143$

When plotting the graph of $\sin(x^x)$ I noticed that there is no plot from about $x=143$. I don't suppose there is a purely mathematical explanation for this? So, why is there no graph in ...
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### What is the best way to write a polynomial in the Bernstein basis?

The Bernstein basis of polynomials of degree $n$ is the set of polynomials of the form $$\binom{n}{k} t^{n-k}(1-t)^k$$ where $0 \leq k \leq n$. What is the best way to transform a given polynomial ...
• 281
389 views

### Strange phenomenon occurring in analytic integration result involving Bessel functions

For the following integral, Integrate[x^2 Exp[-a x^2 - b x^4], {x, -∞, ∞}, Assumptions -> {a > 0, b > 0}] Mathematica gives the following analytic ...
723 views

### Confused by (apparent) inconsistent precision

$$e^{\pi \sqrt{163}} \approx 262537412640768743.99999999999925$$ E^(Pi Sqrt[163.0]) N[E^(Pi Sqrt[163.0]), 35] NumberForm[E^(Pi Sqrt[163.]), 35] returns <...
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679 views

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### Wrong numerical results from LegendreP

{Cos[Pi/180] // N, LegendreP[46, 0.9998476951563913`], LegendreP[46, Cos[Pi/180]] // N} give ...
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262 views

### Is there anyway to remove the noise from the graph in Mathematica?

I am trying to find the root of an equation in Mathematica. But am unable to find it. The Plot function gives a very noisy graph. Can anyone please provide me with a solution to this ...
1 vote
116 views

### Plotting high precision high degree polynomial

When I plot a high degree polynomial such as (available as CloudObject since it is too big to explicitly include): ...
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1 vote
111 views

### Improving working precision of LegendreP[n,x]? [duplicate]

I was trying to evaluate N[LegendreP[5,0.1]] The cell gives me: N[LegendreP[5,0.1]]=0.178829 However I wanted more ...
• 449
1 vote
197 views

### User defined functions and decimal places displayed

I have a couple of complicated user-defined functions, one which calls the other, and I wish to control the number of decimal places displayed when I call the "mother" function. I have tried the ...
• 227
1 vote
120 views

### Calibrating Precision in calculations

As the title says, I encounter an irritating problem which has to do with the accuracy or the precision used in the calculations. To be more specific, I have the following code: ...
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