arctanhvc

Arctanhvc is not a standard or widely used mathematical term. In conventional notation, arctanh denotes the inverse hyperbolic tangent function, defined for scalar inputs x with -1 < x < 1 by atanh(x) = 0.5 ln((1+x)/(1−x)). The addition of the suffix “vc” does not have an established universal meaning in mainstream references, so arctanhvc typically signals a nonstandard or context-specific construction.

In practice, when arctanhvc appears, it is commonly interpreted in one of two ways. One common interpretation is that arctanhvc represents the arctanh function applied componentwise to a vector vc; that is, arctanh(vc) means applying arctanh to each component of the vector. For a vector vc = [v1, v2, ..., vn], this yields arctanh(vc) = [atanh(v1), atanh(v2), ..., atanh(vn)]. The operation requires each component to lie in the interval (-1, 1). The Jacobian of this map is a diagonal matrix with entries 1/(1−vi^2).

An alternative interpretation, when specified in a source, is that arctanhvc denotes a scalar function derived from a vector-valued argument, such as arctanh composed with a particular vector function vc: a context-dependent definition that should be clarified in the source.

Because arctanhvc is not standardized, readers should consult the original text or software documentation to determine the intended meaning and domain. See also arctanh, inverse hyperbolic tangent, and componentwise function application.