Wirtinger derivative
linear partial differential operators (first order constant coefficients) on f(ℂⁿ or ℝ²ⁿ)
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Wirtinger derivative
Summary
Wirtinger derivative ranks in the top 2% of general entities by monthly Wikipedia readership (100 views/month).[1]
Key Facts
- Wilhelm Wirtinger is named after Wirtinger derivative[2].
- Wirtinger derivative's subclass of is recorded as differential operator[3].
- Wirtinger derivative's Freebase ID is recorded as /m/0crgcb6[4].
- Wirtinger derivative's defining formula is recorded as \begin{aligned}\frac\partial{\partial z_i}&=\frac12\left(\frac\partial{\partial x_i}-\mathrm i\frac\partial{\partial y_i}\right)\\frac\partial{\partial\bar z_i}&=\frac12\left(\frac\partial{\partial x_i}+\mathrm i\frac\partial{\partial y_i}\right)\end{aligned}[5].
- Wirtinger derivative's MathWorld ID is recorded as DelBarOperator[6].
- Wirtinger derivative's maintained by WikiProject is recorded as WikiProject Mathematics[7].
- Wirtinger derivative's Microsoft Academic ID is recorded as 104471922[8].
- Wirtinger derivative's in defining formula is recorded as \frac\partial{\partial z_i}[9].
- Wirtinger derivative's in defining formula is recorded as \frac\partial{\partial\bar z_i}[10].
- Wirtinger derivative's in defining formula is recorded as \mathrm i[11].
- Wirtinger derivative's in defining formula is recorded as \frac12[12].
- Wirtinger derivative's in defining formula is recorded as (x_1,y_1,\dotsc,x_n,y_n)[13].
- Wirtinger derivative's in defining formula is recorded as (z_1,\dotsc,z_n)[14].
Why It Matters
Wirtinger derivative ranks in the top 2% of general entities by monthly Wikipedia readership (100 views/month).[1] It has Wikipedia articles in 6 language editions, a strong signal of global cultural recognition.[15] It is known by 4 alternative names across languages and contexts.[16]