Gene

Quantum mechanics

Transformation (genetics)

Pure mathematics

Lauricella hypergeometric series

Confluent hypergeometric function

Statistics

Bilateral hypergeometric series

Generalized hypergeometric function

Appell series

Biochemistry

Hypergeometric distribution

Physics

Mathematics

Hypergeometric function

Bilinear interpolation

Mathematical analysis

Gauss

Chemistry

Hypergeometric function of a matrix argument

Fractional calculus

Basic hypergeometric series

Algebra over a field

Hypergeometric identity

Very recently, the incomplete Pochhammer ratios were defined in terms of the incomplete beta function B y ( x , z ) . With the help of these incomplete Pochhammer ratios, we introduce new incomplete Gauss, confluent hypergeometric, and Appell’s functions and investigate several properties of them such as integral representations, derivative formulas, transformation formulas, and recurrence relations. Furthermore, incomplete Riemann-Liouville fractional integral operators are introduced. This definition helps us to obtain linear and bilinear generating relations for the new incomplete Gauss hypergeometric functions.

Some Incomplete Hypergeometric Functions and Incomplete Riemann-Liouville Fractional Integral Operators