TY - JOUR

T1 - The integral Mittag-Leffler, whittaker and wright functions

AU - Apelblat, Alexander

AU - González-Santander, Juan Luis

N1 - Publisher Copyright:
© 2021 by the authors. Licensee MDPI, Basel, Switzerland.

PY - 2021/12/1

Y1 - 2021/12/1

N2 - Integral Mittag-Leffler, Whittaker and Wright functions with integrands similar to those which already exist in mathematical literature are introduced for the first time. For particular values of parameters, they can be presented in closed-form. In most reported cases, these new integral functions are expressed as generalized hypergeometric functions but also in terms of elementary and special functions. The behavior of some of the new integral functions is presented in graphical form. By using the MATHEMATICA program to obtain infinite sums that define the Mittag-Leffler, Whittaker, and Wright functions and also their corresponding integral functions, these functions and many new Laplace transforms of them are also reported in the Appendices for integral and fractional values of parameters.

AB - Integral Mittag-Leffler, Whittaker and Wright functions with integrands similar to those which already exist in mathematical literature are introduced for the first time. For particular values of parameters, they can be presented in closed-form. In most reported cases, these new integral functions are expressed as generalized hypergeometric functions but also in terms of elementary and special functions. The behavior of some of the new integral functions is presented in graphical form. By using the MATHEMATICA program to obtain infinite sums that define the Mittag-Leffler, Whittaker, and Wright functions and also their corresponding integral functions, these functions and many new Laplace transforms of them are also reported in the Appendices for integral and fractional values of parameters.

KW - Integral Mittag-Leffler functions

KW - Integral Whittaker functions

KW - Integral wright functions

KW - Laplace transforms

UR - http://www.scopus.com/inward/record.url?scp=85121289004&partnerID=8YFLogxK

U2 - 10.3390/math9243255

DO - 10.3390/math9243255

M3 - Article

AN - SCOPUS:85121289004

VL - 9

JO - Mathematics

JF - Mathematics

SN - 2227-7390

IS - 24

M1 - 3255

ER -