Wolfram Function Repository

Instant-use add-on functions for the Wolfram Language

Function Repository Resource:

 EvenFunctionQ

Source Notebook

Determine whether an expression is an even function of the given variable or variables

Contributed by: Wolfram|Alpha Math Team

ResourceFunction["EvenFunctionQ"][expr,x]

returns True if expr is an even function of x, and returns False otherwise.

ResourceFunction["EvenFunctionQ"][expr,{x1,x2,…}]

returns True if expr is an even function under the transformation {x1,x2,…}→{-x1,-x2,…}, and returns False otherwise.

Examples

Basic Examples (13) 

Test whether a basic power function is even:

In[1]:=
ResourceFunction["EvenFunctionQ"][x^2, x]
Out[1]=

Test another power function:

In[2]:=
ResourceFunction["EvenFunctionQ"][x^3, x]
Out[2]=

Test whether a constant function is even:

In[3]:=
ResourceFunction["EvenFunctionQ"][1, x]
Out[3]=

Test whether the absolute value function is even:

In[4]:=
ResourceFunction["EvenFunctionQ"][Abs[x], x]
Out[4]=

Test whether the sine function is even:

In[5]:=
ResourceFunction["EvenFunctionQ"][Sin[x], x]
Out[5]=

Test whether the cosine function is even:

In[6]:=
ResourceFunction["EvenFunctionQ"][Cos[x], x]
Out[6]=

Test whether a Gaussian function is even:

In[7]:=
ResourceFunction["EvenFunctionQ"][Exp[-x^2], x]
Out[7]=

Test a signed Gaussian function:

In[8]:=
ResourceFunction["EvenFunctionQ"][Sign[x] Exp[-x^2], x]
Out[8]=

Test whether a hyperbolic sine function of two variables is even:

In[9]:=
ResourceFunction["EvenFunctionQ"][Sinh[x + y], {x, y}]
Out[9]=

Test whether the hyperbolic tangent function is even:

In[10]:=
ResourceFunction["EvenFunctionQ"][Tanh[x], x]
Out[10]=

Test whether the error function is even:

In[11]:=
ResourceFunction["EvenFunctionQ"][Erf[x], x]
Out[11]=

Test whether a Fresnel integral is even:

In[12]:=
ResourceFunction["EvenFunctionQ"][FresnelC[x], x]
Out[12]=

Test whether a shifted Fresnel integral is even:

In[13]:=
ResourceFunction["EvenFunctionQ"][FresnelC[x] + 1, x]
Out[13]=

Scope (4) 

For a function of multiple variables, parity is determined based on the behavior of the function under the transformation {x,y,..}→{-x,-y,..}. Find the parity of a function of two variables:

In[14]:=
ResourceFunction["EvenFunctionQ"][Cosh[x + y], {x, y}]
Out[14]=
In[15]:=
ResourceFunction["EvenFunctionQ"][Sinh[x + y], {x, y}]
Out[15]=

Find the parity of a function of three variables:

In[16]:=
ResourceFunction["EvenFunctionQ"][Sin[x y z], {x, y, z}]
Out[16]=

Wrapping one of the variables in Abs converts this to an even function:

In[17]:=
ResourceFunction["EvenFunctionQ"][Sin[x y Abs[z]], {x, y, z}]
Out[17]=

Show that an implicitly-defined circle is even in both x and y:

In[18]:=
ResourceFunction["EvenFunctionQ"][x^2 + y^2, {x, y}]
Out[18]=

Publisher

Wolfram|Alpha Math Team

Version History

  • 4.0.0 – 23 March 2023
  • 3.0.0 – 01 April 2020
  • 2.0.0 – 06 September 2019
  • 1.0.0 – 09 July 2019

Related Resources

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