2F1c

2F1c is a term that may refer, in mathematical contexts, to the Gauss hypergeometric function, most commonly written as 2F1(a,b;c;z). The two numerator parameters a and b and the single denominator parameter c determine a function of the complex variable z. The standard series definition is 2F1(a,b;c;z) = sum_{n=0}^∞ (a)_n (b)_n / (c)_n · z^n / n!, where (q)_n is the rising Pochhammer symbol. The series converges for |z| < 1 and can be extended by analytic continuation; if c is a nonpositive integer, the series terminates and the function becomes a polynomial in z.

In common mathematical practice, 2F1c is not a standardized notation. It may appear as a shorthand or a typographical variant for 2F1(a,b;c;z) in certain texts or software outputs, but it is not recognized as a separate function in mainstream literature. When encountered, the meaning should be inferred from context to determine whether it refers to the standard Gauss hypergeometric function with explicit parameters or to some other, context-specific usage.

The Gauss hypergeometric function satisfies Gauss’s differential equation: z(1−z) f'' + [c − (a+b+1) z] f' − a b f = 0, and it encompasses many special functions as particular cases (for example, certain choices of a, b, and c yield elementary functions, Legendre functions, or elliptic integrals). It is widely used in mathematical analysis, physics, and geometry due to its rich analytic structure and connections to transformation formulas and monodromy.

In summary, 2F1c is not a standard independent object; when seen, it most often denotes the Gauss hypergeometric function 2F1(a,b;c;z) in a nonstandard shorthand, with exact meaning clarified by context.