A new sequence of numbers called Chintaginjala numbers, Chintaginjala polynomials and their properties.

Abstract

Euler, Bernoulli and Gnocchi numbers are sequences of signed rational numbers, defined by various exponential generating functions. In this paper, I am introducing a new number sequence of signed rational numbers, polynomials called Chintaginjala numbers and Chintaginjala polynomials by using different generating function. I used McLaurin’s infinite series for this number system. In this theory we find the relation between Chitaginjala numbers and Bernoulli’s numbers. Chintaginjala numbers appear in twelve infinite series expansions. I derive 0 to 20 Chintaginjala numbers and 0 to 10 Chintagijala polynomials. In this study we derive the derivative and integration properties of Chintaginjala numbers, chintaginjala polynomials also we derive some forward difference(Delta) properties of Chitaginjala polynomials to calculate sum of n powers of n consecutive natural numbers. We also draw the graphs of first five Chintaginjala polynomials.