Wolfram Research

Function Repository Resource:

OddFunctionQ

Source Notebook

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

Contributed by: Wolfram|Alpha math team

ResourceFunction["OddFunctionQ"][f[x],x]

returns True if f[x] is an odd function of x, and returns False otherwise.

Details and Options

A function is odd if f(-x)=-f(x) for all x.

Examples

Basic Examples

Test whether a basic power function is odd:

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

Test another power function:

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

Applications

Test whether a constant function is odd:

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

Test whether the absolute value function is odd:

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

Test whether the sine function is odd:

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

Test whether the cosine function is odd:

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

Test whether a Gaussian function is odd:

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

Test a signed Gaussian function:

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

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

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

Test whether the hyperbolic tangent function is odd:

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

Test whether the error function is odd:

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

Test whether a Fresnel integral is odd:

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

Test whether a shifted Fresnel integral is odd:

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

Resource History

See Also

License Information