sqrtDn

sqrtDn is not a standard mathematical constant or function, but a notational shorthand that may be used in some texts to denote the principal square root of the n-th term of a sequence D = {D_n}. The precise meaning of sqrtDn depends on the context and how D_n is defined in a given work.

Definition and domain: If D = {D_n} is a sequence of real numbers and D_n is nonnegative, then sqrtDn(n) is commonly understood as sqrt(D_n), the principal (nonnegative) square root of the n-th term. If D_n is negative, the square root is not real; in such cases sqrt(D_n) can be understood in the complex sense, or the index n may be restricted to values with D_n >= 0.

Variations and interpretations: In some contexts, D_n might denote a matrix, operator, or another mathematical object, in which case sqrt(D_n) would refer to a matrix square root or an operator square root, and sqrtDn as a shorthand for evaluating that expression at index n. When D_n is a scalar sequence, sqrtDn is effectively the sequence of square roots: sqrtDn = {sqrt(D_n)}.

Examples: If D_n = n^2 + 1, then sqrtDn(n) = sqrt(n^2 + 1). If D_n = 4 for all n, then sqrtDn(n) = 2 for every n.

Computational notes: Compute D_n according to its definition, then apply a standard square-root algorithm, ensuring the argument is nonnegative for real arithmetic or handling complex results if necessary.

See also: sqrt, sequences, matrix square root, complex square root.