# Tag Info

Accepted

### Closed form of an integral using Mathematica or otherwise

We can substitute $\left\{~ u = 1 - xy,~ v = y ~\right\}$ using IntegrateChangeVariables to get a nice expression for the integral: ...
• 5,042

### Solving third order DE from fluid dynamics

One can observe that the original equation can be simply integrated twice w.r.t. $x$, this yields: $$y'(x)+y(x)^2-c_2\; x+c_1=0$$ We could choose arbitrarily signs of constants, now solving it ...
• 57.7k
Accepted

### An integral using Mathematica or otherwise

Using: $$\sum _{\alpha =0}^{-A} \binom{-A}{\alpha } (u v w x y)^{\alpha } (1-w)^{-A-\alpha }=(1-w+u v w x y)^{-A}$$ where: A=2 Then: ...
• 14.9k

### Binomial[-1,-1]

Version 14.1 introduced PascalBinomial, which preserves Pascal's identity for all integer values, and uses a different definition for negative integer $n$ than <...
• 30.6k
Accepted

$Version (* "14.0.0 for Mac OS X ARM (64-bit) (December 13, 2023)" *) Clear["Global`*"] w = c Sqrt[kz^2 + q^2]; Use ... • 161k 6 votes ### Calculation time too long for FoxH ... • 14.9k 6 votes ### How to transform this combination of$ _2F_1 $? It can be simplifed more. Using undocumented command: ... • 14.9k 5 votes ### How to compile inverse error function? You can port one of the C algorithms for erfinv to Mathematica. Here, I've used @njuffa's code for erfinvf, which is a single-... • 30.6k 5 votes Accepted ### What formula does Mathematica use for PolyGamma function of complex order? For negative integer and negative noninteger Mathematica uses formula: $$\psi ^{(n)}(x)=\frac{\int_0^x (x-t)^{-n-2} \text{log\... • 14.9k 5 votes ### Using NDSolve on the Painlevé equations By the method in this article A method for calculating the Painlevé transcendents, poles of second-order ODE can be passed by auxiliary functions u[x] and ... • 2,200 5 votes Accepted ### How to compile inverse error function? You could use OpenCLLink if you need to run this on a huge amount of data and want to use your GPU: ... • 25.6k 5 votes Accepted ### Using FindSequenceFunction to solve the integral of the product of Legendre polynomials and power functions ... • 161k 5 votes ### The conversion equation between BesselI and BesselJ These are not same for all input. e1 = BesselI[v, x] e2 = BesselJ[v, I x]/I^v Assuming[Element[v, Reals] && x > 0, FullSimplify[e1 - e2]] (* 0 *) You ... • 149k 5 votes Accepted ### Are there any commands besides NSolve for solving equations which involve product logarithm? The first equation only depends on d. Therefore, we solve it first (We need to rationalize to prevent numerical problems): ... • 54.6k 5 votes ### Expressing elliptic \lambda^*(r) with radicals ... • 161k 5 votes ### Why do I get different results for the products of two identical expressions? Bug in NProduct maybe. For that second one, rote conversion to logs, then NSum, then Exp ... • 59.8k 5 votes ### Issue in HypergeometricPFQ function: It's NOT a strange behavior of HypergeometricPFQ[{1/2 - n/2, 1 - n/2}, {3/2, 1 - n}, -n]. HypergeometricPFQ works fine. I made a ... • 14.9k 5 votes Accepted ### How to verify a FactorialPower identity? Another way is to use FindSequenceFunction We start from FactorialPower[x - i*k, n, m*k] and compute a few values, say ... • 16.4k 5 votes ### How to port Matlab/Python's multivariate FoxH implementation in Mathematica? Now it works. The result is consistent with Python/MATLAB. Any help for accelerating the Mathematica code would be greatly appreciated. ... • 1,902 5 votes ### An integral using Mathematica or otherwise I tried it with 2 and 3 variables ... • 3,169 4 votes ### Why can't NSolve solve for the obvious zeros? Fixed in Version 14.0 ... • 149k 4 votes ### Can the Debye functions be implemented using built-in functions? This only partially answers your question so I'll delete if it is not what you're looking for. The first type of functions, D^{(1)}_n (x) satisfy the differential equation$$D^{'(1)}_n (x) = \frac{x^... • 5,042 4 votes ### Numerical integration of MeijerG function in the form MeijerG[{{-2,-8.5,-3.5},{}},{{0},{-1.5}},theta] You can just use Integrate to evaluate the integral by adding the option PrincipalValue -> True, like ... • 2,200 4 votes Accepted ### Simplify inverse of function ... • 161k 4 votes ### Mathematica cannot solve this complicated integration This integral can be expressed by Leaky Aquifer function or Generalization of the Incomplete Gamma function. Let's consider: ... • 14.9k 4 votes Accepted ### How to integrate Legendre polynomials with parameters? ... • 161k 4 votes Accepted ### Expressions in PlotLegends ... • 56.1k 4 votes ### Is it possible to express$\text{Li}_2(-\frac18(-i+\sqrt{15})+\text{Li}_2(\frac18 (i+\sqrt{15})\$ as an explicit real expression (not numeric)?

The expression can be expressed as infinite sum. All the sums are pretty much the same only in different form and all produce the same terms/summands. ...
• 20.9k
Accepted

### Is it possible to have the asymptotics of this function?

The following proves your expectations. ...
• 27.7k