Questions tagged [special-functions]

Questions on the special mathematical functions implemented in Mathematica.

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Solving of Equation which contains Hypergeometric Function 2F1

I am trying to solve this equation where I need the solution of K in term of v ...
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What series does Mathematica use for Hypergeometric1F1?

I'm trying to get an analytical expression for Hypergeometric1F1[-a, 1/2, X] Provided a is an integer number. I tried adding ...
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What is the representation of the Harmonic Number being used by Mma in this result?

The Fourier Transform of the function F[x_] = (m/Sqrt[\[Lambda]])*Tanh[(Sqrt[x^2]*m)/Sqrt] where all variables are real, and $m>0$ is given by (Mma 11.0) ...
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Plotting the inverse function of a complicated function

So I have a function F[x_] = Assuming[{Element[x, Reals], -1 < x < 1}, Integrate[1/Sqrt[(x^2 - 1)^2 + alpha*x], x]] I'm now interested in the ...
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Computing Hypergeometric Funtion of Matrix Argument [duplicate]

I'm new to Mathematica and unsure of how to compute functions or set up definitions. I'd like to do some computations with the $_1F_1$ hypergeometric function of matrix argument as in the Koev and ...
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How do I make InverseBetaRegularized function behave the same in Mathematica 11.3 compared to 11.2?

In Mathematica 11.3: InverseBetaRegularized[0.001, 4501, 500] Never finishes calculating. ...
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Plot a function defined on terms on its value on an interval

Besicovitch-Ursell family of fractal functions uses the following auxiliar definition: $\phi(x) = 2x$ on $[0,1/2]$. $\phi(-x) = \phi(x+1)$ otherwise. Is there a way to plot this in mathematica?
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Closed form solutions to functions involving Erfc

Is there a better way to get a closed form solution in terms of sigma? I've already attempted a significant amount of simplification up to this point and am unsure ...
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How to convert solution from ParabolicCylinderD to Bessel functions?

I am trying to verify my hand solution to an ODE. The solution I got is in terms of Bessel functions. Maple gives same solution. Mathematica gives the solution in terms of ParabolicCylinderD which I ...
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Flaky pattern-matching for Mittag-Leffler sums?

This sum correctly gives the Mittag-Leffler function: Sum[z^k/Gamma[α*k + α], {k, 0, ∞}] MittagLefflerE[α, α, z] Simply factoring the argument of ...
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Sum Over Solutions to an Equation

Two Related Questions Is there any general built-in functionality for computing a sum over solutions to an equation? This is common in number theory. For example, computing sums of the following form....
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Getting values of EllipticK with arguments that are very near 1

I need to evaluate EllipticK[m] very close to 1. However, when I get too close to 1 the function defaults to the exact solution for 1 , which is ...
564 views

How to prevent Mathematica rounding extremely small numbers to zero?

I have a function that, while the maths itself is unimportant, at certain values it results in a very large number multiplying a very small number. E.g. 10^450000 * 10^-449998. As you can see, this ...