Parallel (operator)

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The parallel operator $\|$ (pronounced "parallel") is a mathematical function which is used especially as shorthand in electrical engineering. It represents the reciprocal value of a sum of reciprocal values and is defined by:

${\begin{array}{rlcl}\|:\ &{\overline {\mathbb {C} }}\times {\overline {\mathbb {C} }}&\to &{\overline {\mathbb {C} }}\\&(a,b)&\mapsto &a\|b={\frac {1}{{\frac {1}{a}}+{\frac {1}{b}}}}\end{array}}$

That is, it gives half of the harmonic mean of two numbers a and b.

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