Hicksian demand function
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In microeconomics, a consumer's Hicksian demand function h(p,u) gives the cheapest bundle under a price level p for which the consumer derives a utility level of at least u. The function is named after John Hicks.
Hicksian demand functions are often convenient for mathematical manipulation because they don't require income or wealth to be represented. However, Marshallian demand functions of the form x(p,w) that describe demand given prices p and income w are easier to observe directly. The two are trivially related by
where e(p,u) is the expenditure function, and by
where v(p,w) is the indirect utility function. They are more fundamentally related by the Slutsky equation.
The Hicksian demand function is intimately related to the expenditure function. If the consumer's utility function u(x) is locally nonsatiated and strictly convex, then 
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