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In [[mathematics]], a '''homogeneous function''' is a [[function of several variables]] such that, if all its arguments are multiplied by a [[scalar (mathematics)|scalar]], then its value is multiplied by some power of this scalar, called the '''degree of homogeneity''', or simply the ''degree''; that is, if {{mvar|k}} is an integer, a function {{mvar|f}} of {{mvar|n}} variables is homogeneous of degree {{mvar|k}} if
:<math>f(sx_1,\ldots, sx_n)=s^k f(x_1,\ldots, x_n)</math>
for every <math>x_1, \ldots, x_n,</math> and <math>s\ne 0 ,</math> <math>s\ne 1.</math>
For example, a [[homogeneous polynomial]] of degree {{mvar|k}} defines a homogeneous function of degree {{mvar|k}}.
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