Kronecker delta

The Kronecker delta is a symbol used across many areas of mathematics. In these notes it is defined as follows: general

𝛿 𝑘 = [𝑘 = 0] = {1 𝑘 = 0 0 𝑘 \neq 0

where we have used an Iverson bracket, and for multiple subscripts

𝛿 𝑘, 𝑗 1, \dots, 𝑗 𝑛 = 𝑛 \prod 𝑖 = 1 𝛿 𝑘 - 𝑗 1 = [𝑘 = 𝑗 1 = \dots = 𝑗 𝑛] = {1 𝑘 = 𝑗 1 = \dots = 𝑗 𝑛 0 o t h e r w i s e

See also Dirac delta for a continuous (distributional) analogue.