Classical Nonelementary Integrals and Dominating Sequential Functions
Dharmendra Kumar Yadav *
University Department of Mathematics, Lalit Narayan Mithila University, Darbhanga, Bihar, India.
Shivjee Yadav
University Department of Mathematics, Lalit Narayan Mithila University, Darbhanga, Bihar, India.
*Author to whom correspondence should be addressed.
Abstract
The aim of the paper is to express some well known nonelementary integral functions like sine integral, cosine integral, Dirichlet integral, Faddeeva function, Fried Conte function, Jackson function, Dawson integral, Fresnel function, Sitenko function, Gordeyev integral, error function, complementary error function, exponential integral, and logarithmic integral in terms of sequential and dominating sequential functions. The expressions in terms of sequential and dominating sequential functions will be the possible solutions (or integrals) of those nonelementary functions. In the study we found that except Plasma Dispersion Function, (Jackson) Function and Gordeyev Integral all other classical nonelementary integral functions discussed in the paper are expressible terms of sequential and dominating sequential functions. In last section a scope of future research has also been proposed.
Keywords: Nonelementary integral functions, sequential functions, dominating sequential functions