TY - JOUR
AU - P. K. Ray
PY - 2017/04/25
Y2 - 2020/12/03
TI - Balancing polynomials and their derivatives
JF - Ukrainsâ€™kyi Matematychnyi Zhurnal
JA - Ukr. Mat. Zhurn.
VL - 69
IS - 4
SE - Research articles
DO -
UR - http://umj.imath.kiev.ua/index.php/umj/article/view/1715
AB - We study the generalization of balancing numbers with a new sequence of numbers called $k$-balancing numbers. Moreover,by using the Binet formula for $k$-balancing numbers, we obtain the identities including the generating function of thesenumbers. In addition, the properties of divisibility of these numbers are investigated. Further, balancing polynomials thatare natural extensions of the $k$-balancing numbers are introduced and some relations for the derivatives of these polynomialsin the form of convolution are also proved.
ER -