## Tag: special-functions

58 What is the difference between a few simplification techniques? 2012-04-20T01:22:13.203

45 About multi-root search in Mathematica for transcendental equations 2012-05-17T07:52:59.270

43 Fast Spherical Harmonics radiative transfer 2012-09-18T10:43:16.673

37 Is there a Mathematica API for the functions.wolfram site? 2011-05-31T04:02:40.987

35 Peirce's quincuncial projection 2013-04-29T04:22:10.680

33 Is MathieuC for moderately large imaginary arguments broken? 2015-05-09T17:06:19.853

32 Visualizing vector spherical harmonics 2013-05-12T05:50:56.107

27 How to improve performance of BesselJ to the level of GSL? 2015-06-02T10:40:20.277

21 Why does Mathematica give the wrong answer when integrating? 2012-03-08T19:31:24.380

20 Incorrect result from Integrate 2013-11-03T20:20:31.523

20 Expansion of a hypergeometric function takes ages with Mathematica 9 and 10 (regression?) 2015-03-29T18:28:43.227

20 Eisenstein Series in Mathematica? 2015-07-29T14:33:57.393

19 Numerical underflow for a scaled error function 2012-04-03T08:28:53.813

19 Incorrect results for elementary integrals when using Integrate 2012-04-25T08:50:37.617

18 Speeding up trigonometric integral 2012-11-15T17:15:27.490

18 How to represent a continuous monotonic phase of Airy functions? 2013-10-08T19:29:16.787

18 Creating a Mathieu stability diagram 2014-04-24T23:06:20.830

17 What kind of hypergeometric function is it? 2013-05-22T16:14:03.403

16 How to enlarge Mathematica's knowledge about certain functions? 2013-09-30T13:10:53.780

16 How to define Mc and Ms Mathieu functions in terms of MathieuC and MathieuS? 2015-05-01T19:06:30.540

16 How can I get the solutions of $x^n-x-t=0$ in hypergeometric form? 2015-11-02T14:36:04.897

16 Backslide in NSolve in V11.1? 2017-04-18T03:12:46.387

15 Solve an integral equation numerically 2012-12-07T06:04:48.693

15 How to plot Ramanujan's continued fraction in Mathematica? 2015-06-20T18:27:49.857

15 SphericalHarmonicY does not seem to be an eigenfunction of the spherical harmonic equation 2015-12-18T00:40:03.573

15 How do I numerically evaluate and plot the Fabius function? 2016-07-09T06:12:09.057

15 How to convert this term to a Hypergeometric function? 2019-10-19T07:57:15.417

14 Implementing a compilable Faddeeva function of complex argument 2017-07-31T12:48:18.843

14 Terrible accuracy of DawsonF 2018-09-20T14:34:48.363

13 Extra factors appear when evaluating Euler integrals 2012-07-19T19:36:58.233

13 Compiling the VoigtDistribution PDF 2013-02-20T17:17:45.750

13 Numerically solve 2nd order differential equation with singularity 2013-05-09T08:12:13.567

13 Find asymptotics of $\sum\limits_{i=0}^{n/3} 2^i \binom{n-i-1}{\frac{2n}{3}-1}$ 2013-09-24T12:02:10.377

13 Faster and smoother contourplot? 2017-02-26T21:46:44.547

13 Looping through all functions defined in Mathematica 2020-05-10T04:34:09.503

12 Why can't I change the value of MaxRecursion in NIntegrate when integrating BesselJ? 2013-05-07T16:19:47.170

12 Why NIntegrate is badly-behaved on $J_{\frac{9}{2}}(x)$ by default? 2016-06-08T07:59:48.607

12 Getting wrong limit with Bessel 2016-11-09T00:00:52.253

12 Assumptions allowing to calculate an elliptic integral 2016-12-08T06:14:36.507

12 Possible bug in finite sum over inverse squares $\sum\limits_{i=1}^n \frac{1}{(x (n-i)+i)^2}$ 2020-05-07T19:28:43.757

11 problem with coloring spherical harmonics 2012-12-18T13:03:02.450

11 Integrating a BesselJ integrand to obtain the same result as Maple 16 2013-11-28T05:48:31.007

11 Binomial[-1,-1] 2014-04-09T10:38:07.437

11 Expanding derivatives of hypergeometric functions 2014-07-23T22:26:13.297

11 Fine tuning compiled code that computes dilogarithm function 2014-10-11T12:39:01.570

11 Wrong Limit with LaguerreL 2015-05-22T08:10:40.937

11 Differential equations with rational functions as solution 2016-02-10T22:37:42.713

11 Vastly incorrect answers obtained by increasing WorkingPrecision with modified Bessel functions 2016-05-24T02:19:52.130

11 Solving quintic in radicals 2016-12-15T01:39:44.990

11 How can I translate a MathWorld statement into Mathematica syntax? 2017-12-17T12:20:22.603

11 Elliptic Integrals: Mathematica and Gradshteyn and Ryzhik 2019-12-11T12:39:51.853

10 Creating Plots for a Family of Solutions 2012-02-19T03:59:37.110

10 Series expansion with irrational power 2012-08-30T03:30:37.937

10 Is my expression too complicated for FullSimplify or am I doing something wrong? 2012-09-27T23:54:56.150

10 Multi-Factorial and Series with Triple-factorial terms 2012-11-21T12:57:44.810

10 Visualizing vector-spherical waves 2013-05-19T22:08:22.600

10 Are solid spherical harmonics implemented in Mathematica? 2014-04-11T17:34:49.030

10 Mathieu function periodicity problem 2014-09-03T02:57:49.493

10 Plotting a Bifurcation diagram 2015-10-02T06:26:47.763

10 Speed up construction of a dense matrix 2016-01-08T00:19:53.130

10 Mathematica implementation of Zeilberger's algorithm (previously done in Maple) 2016-06-24T17:48:57.390

10 is it possible to change/customize some conversions done by TeXForm? 2017-08-17T02:26:51.640

10 Evaluating Lauricella functions in Mathematica? 2017-08-24T14:53:19.453

10 The numerics of FresnelS[] 2020-08-03T15:02:16.943

9 Hankel Transform integrals won't work in Mathematica 2012-02-18T13:10:36.790

9 Checking if the roots of a function are real 2012-06-13T07:49:11.907

9 Finding the roots of Hypergeometric1F1[] 2012-08-02T22:04:59.087

9 Implementation of Incomplete Fermi-Dirac Integral in Mathematica 2012-10-23T06:29:54.997

9 Integrating over Bessel Function erroneous? (Hankel Transform) 2013-02-02T12:59:39.773

9 How to simplify an expression with special functions to zero 2013-05-15T15:43:16.710

9 Numerical instability in cosh and sinh - integral functions 2013-12-13T10:46:39.117

9 Substituting values in 3j symbols 2014-08-02T13:21:39.537

9 Plotting an expression involving the inverse error function 2014-11-01T19:16:30.337

9 MacDonald formula for Modified Bessel Functions 2014-11-12T08:30:33.977

9 Number of divisors visualized with the QPochhammer function, how to improve performance of code? 2015-01-04T19:03:15.737

9 Derivative of the Dedekind eta function fails to compute with errors I don't understand 2015-11-15T19:53:39.190

9 Can your Mathematica do the following integral? 2015-12-26T04:05:30.047

9 Labeling solutions of an Eigenvalue equation involving Bessel functions 2016-01-01T20:27:34.313

9 Show how Mathematica defines a function 2016-04-12T17:47:28.443

9 Visualizing the primes with the Riemann Zeta function 2016-12-13T00:58:35.757

9 NDEigenvalues vs. FindRoot for finding the eigenvalues of Airy equation? 2018-10-05T05:46:44.410

9 Bug in SumConvergence 2018-12-16T08:04:05.570

9 How could this asymptotic expansion be obtained? 2019-05-06T05:32:35.723

9 Closed form of product of Gamma function 2019-11-18T19:34:10.347

9 Possible bug involving derivative of BesselI 2020-02-22T01:06:11.020

9 Numerically evaluating parameter derivatives of a hypergeometric function 2020-12-23T08:03:30.970

8 Inverse Laplace transform not obtained 2012-06-27T23:40:13.083

8 Erfc Not Returning Results Specified in Documentation 2013-03-05T03:55:56.253

8 Prove an identity in quantum harmonic oscillator 2013-12-09T22:40:33.087

8 Why does N[Re@f] give complex result? 2014-08-28T03:37:30.467

8 On the definition of the associated Legendre polynomials 2014-09-06T14:46:47.953

8 Diverging solution to coupled second order ODEs from NDSolve 2015-04-23T14:37:21.973

8 Generating terms of the Stirling series 2015-06-24T09:29:53.810

8 Evaluating a Series expansion of PolyLog function 2015-06-25T18:30:03.467