# Tagged Questions

Questions on the special mathematical functions implemented in Mathematica.

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### How to take conjugate of a function?

Naïvely this is what happens and it obviously is not helpful! ...
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### Fast Spherical Harmonics radiative transfer

This is a rather specific question and I apologize for spamming you with some lengthy code. But it could be interesting for some reader and maybe you can help out, so please bear with me. I am using ...
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### Why can't I change the value of MaxRecursion in NIntegrate when integrating BesselJ?

Bug introduced in 8.0.4 or earlier and persists through 10.0.2. I am trying to evaluate this integral numerically $$\int_0^{\infty } J_0(q R) \tanh(q) \, \mathrm{d}q$$ for large values of $R$. ...
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### Function for importing and plotting data from excel spreadsheet

I know this must be a very basic question, but I could not find any answers. I need to create a function that: 1) imports data from an Excel Spreadsheet, 2) assign specific information from this xlsx ...
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### Sum over Binomials and Gammas

Given the function, ...
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### General function for the expansion of a polynomial of operators

This question is motivated by a Quantum mechanical problem - but in explaining the problem - I assume no knowledge of quantum mechanics. I want to define a function that can expand and simplify the ...
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### Complete definition of special functions in Mathematica [closed]

How can one display the actual integral involved in special functions like this MarcumQ[2, a, b] in Mathematica?
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### Defining functions that depend upon other functions which depend upon other functions and so on

The problem is that I have to evaluate functions, that take output from previous functions, and combine them to form new functions, and do some operations and evaluate the value at new function. But, ...
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### How to find and verify relationships between functions?

MMa gave me a complicated result involving Hypergeometric0F1's. It was much less complicated after I discovered this identity: ...
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### Probability of multivariate normal being positive on each coordinate

How can I find the probability that each coordinate of a specified multivariate normal distribution is positive? I tried the following, which I believed should work ...
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### EllipticF reduction

Is it possible to reduce the following Z to Legendre form Elliptic integral of the First kind? $$\int \dfrac {\sec u\; du } {\sqrt{ (1- {(\nu \tan u)}^2 }} ..(1*)$$ With ...
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### How to make the result of Piecewise be a closed interval?

Description This question comes from two questions. Namely Q1 and Q2 The defintion of B-Spline basis function as shown below: Let $\vec{U}=\{u_0,u_1,\ldots,u_m\}$ a nondecreasing sequence of real ...
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I found a nice paper about inverse vector operators here. I have successfully implemented a Mathematica function for most of them, however I can't figure out how to do inverse gradient (page 7 in the ...
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### Using Fold to show stages of Euler product formula

I would like to recursively replicate each stage of the Euler product proof. This does it: ...
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### Is there a LogBeta function like the LogGamma?

In a computation, I need Log[Beta[alpha+j,beta-j+n]] of some kind. Is there a LogBeta function built-in to avoid any under/over ...
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I wanted the inverse logarithmic intgral, so I typed InverseFunction[LogIntegral] and received the expected symbolic answer. But when I try to integrate it or ...
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### Symbolic derivatives of special functions yield incorrect results

When I evaluate with Mathematica this expression D[ Abs[ Zeta[x + I y]], {x, 2}] + D[ Abs[ Zeta[x + I y]], {y, 2}] 0 the ...