Wolfram Function Repository

Instant-use add-on functions for the Wolfram Language

Function Repository Resource:

 FoxHForm

Source Notebook

Convert a mathematical expression into an equivalent expression with head FoxH

Contributed by: Paco Jain & Oleg Marichev

ResourceFunction["FoxHForm"][f,z]

expresses the function f, written in terms of the independent variable z, in terms of FoxH when possible.

Details

The result of FoxH form will either return an expression involving Inactive[FoxH] or will return unevaluated if no such expression can be found. The Inactive wrapper is to prevent auto-evaluation of FoxH into simpler functions and can be removed with Activate.

Examples

Basic Examples (2) 

Get the Fox H form of a trigonometric function:

In[1]:=
ResourceFunction["FoxHForm"][Sin[z], z]
Out[1]=

Activating the result allows the FoxH to evaluate, giving back the original function:

In[2]:=
Activate[%]
Out[2]=

Represent BesselJ in terms of FoxH:

In[3]:=
ResourceFunction["FoxHForm"][BesselJ[1, a x], x]
Out[3]=

Recover the original function using Activate:

In[4]:=
Activate[%]
Out[4]=

Scope (11) 

Elementary Functions (5) 

Rational functions:

In[5]:=
ResourceFunction["FoxHForm"][1/(x^2 + 1), x]
Out[5]=
In[6]:=
ResourceFunction["FoxHForm"][1/(2 x + 3), x]
Out[6]=

Algebraic functions:

In[7]:=
ResourceFunction["FoxHForm"][1/(Sqrt[x] + 1), x]
Out[7]=

Trigonometric functions:

In[8]:=
ResourceFunction["FoxHForm"][Sin[a x], x]
Out[8]=
In[9]:=
ResourceFunction["FoxHForm"][Cos[a x + d], x]
Out[9]=

Linear combination of trigonometric functions:

In[10]:=
ResourceFunction["FoxHForm"][2 Sin[x] + Cos[x], x]
Out[10]=

Inverse trigonometric and hyperbolic functions:

In[11]:=
ResourceFunction["FoxHForm"][ArcSin[x], x]
Out[11]=
In[12]:=
ResourceFunction["FoxHForm"][ArcTanh[x], x]
Out[12]=

Special Functions (6) 

Airy functions:

In[13]:=
ResourceFunction["FoxHForm"][AiryAi[x], x]
Out[13]=
In[14]:=
ResourceFunction["FoxHForm"][AiryBi[x], x]
Out[14]=

Bessel functions:

In[15]:=
ResourceFunction["FoxHForm"][BesselJ[n, x], x]
Out[15]=
In[16]:=
ResourceFunction["FoxHForm"][BesselK[n, x], x]
Out[16]=

Legendre functions:

In[17]:=
ResourceFunction["FoxHForm"][LegendreQ[n, x], x]
Out[17]=

Mittag-Leffler functions:

In[18]:=
ResourceFunction["FoxHForm"][MittagLefflerE[n, x], x]
Out[18]=
In[19]:=
ResourceFunction["FoxHForm"][MittagLefflerE[n, c, x], x]
Out[19]=

Hypergeometric functions:

In[20]:=
ResourceFunction["FoxHForm"][Hypergeometric2F1[a, b, c, x], x]
Out[20]=

Elliptic integrals:

In[21]:=
ResourceFunction["FoxHForm"][EllipticK[m], m]
Out[21]=
In[22]:=
ResourceFunction["FoxHForm"][EllipticE[m], m]
Out[22]=

Properties and Relations (1) 

If a FoxH representation cannot be found, the function returns unevaluated:

In[23]:=
ResourceFunction["FoxHForm"][Sqrt[1 - Cosh[z]], z]
Out[23]=

Publisher

Wolfram|Alpha Math Team

Requirements

Wolfram Language 13.0 (December 2021) or above

Version History

  • 1.1.0 – 05 April 2024
  • 1.0.0 – 03 April 2024

Related Resources

Author Notes

To view the full source code for this and related functions, evaluate the following:

In[1]:=
SystemOpen[ DirectoryName[ FindFile["WolframAlphaMath`SpecialFunctionsAndCalculus`"]]]

License Information