scholarly journals Fibonacci Series from Power Series

2020 ◽  
Author(s):  
Kunle Adegoke
Keyword(s):  
Power Series ◽  
Infinite Series ◽  
Gamma Function ◽  
Bernoulli Numbers ◽  
Trigonometric Functions ◽  
Euler Numbers ◽  
Lucas Numbers ◽  
Fibonacci Series ◽  
Digamma Function ◽  
Inverse Trigonometric Functions

We show how every power series gives rise to a Fibonacci series and a companion series involving Lucas numbers. For illustrative purposes, Fibonacci series arising from trigonometric functions, inverse trigonometric functions, the gamma function and the digamma function are derived. Infinite series involving Fibonacci and Bernoulli numbers and Fibonacci and Euler numbers are also obtained.

scholarly journals Fibonacci series from power series

2021 ◽  
Vol 27 (3) ◽  
pp. 44-62
Author(s):  
Kunle Adegoke ◽  
Keyword(s):  
Power Series ◽  
Infinite Series ◽  
Gamma Function ◽  
Bernoulli Numbers ◽  
Trigonometric Functions ◽  
Euler Numbers ◽  
Lucas Numbers ◽  
Fibonacci Series ◽  
Digamma Function

We show how every power series gives rise to a Fibonacci series and a companion series involving Lucas numbers. For illustrative purposes, Fibonacci series arising from trigonometric functions, the gamma function and the digamma function are derived. Infinite series involving Fibonacci and Bernoulli numbers and Fibonacci and Euler numbers are also obtained.

scholarly journals Turán type inequalities for generalized inverse trigonometric functions

Filomat ◽  
2015 ◽  
Vol 29 (2) ◽  
pp. 303-313 ◽  
Author(s):  
Árpád Baricz ◽  
Ali Bhayo ◽  
Matti Vuorinen
Keyword(s):  
Laplace Operator ◽  
Generalized Inverse ◽  
Type Inequality ◽  
Trigonometric Functions ◽  
Hyperbolic Functions ◽  
Digamma Function ◽  
One Dimensional ◽  
Turán Type Inequalities ◽  
The One ◽  
Inverse Trigonometric Functions

In this paper we study the inverse of the eigenfunction sinp of the one-dimensional p-Laplace operator and its dependence on the parameter p, and we present a Tur?n type inequality for this function. Similar inequalities are given also for other generalized inverse trigonometric and hyperbolic functions. In particular, we deduce a Tur?n type inequality for a series considered by Ramanujan, involving the digamma function.

Identities related to special polynomials and combinatorial numbers

Filomat ◽  
2017 ◽  
Vol 31 (15) ◽  
pp. 4833-4844 ◽  
Author(s):  
Eda Yuluklu ◽  
Yilmaz Simsek ◽  
Takao Komatsu
Keyword(s):  
Generating Functions ◽  
Functional Equations ◽  
Stirling Numbers ◽  
Bernoulli Numbers ◽  
Euler Numbers ◽  
Special Polynomials ◽  
Central Factorial Numbers

The aim of this paper is to give some new identities and relations related to the some families of special numbers such as the Bernoulli numbers, the Euler numbers, the Stirling numbers of the first and second kinds, the central factorial numbers and also the numbers y1(n,k,?) and y2(n,k,?) which are given Simsek [31]. Our method is related to the functional equations of the generating functions and the fermionic and bosonic p-adic Volkenborn integral on Zp. Finally, we give remarks and comments on our results.

scholarly journals Some Identities Involving the Fubini Polynomials and Euler Polynomials

Mathematics ◽  
2018 ◽  
Vol 6 (12) ◽  
pp. 300 ◽  
Author(s):  
Guohui Chen ◽  
Li Chen
Keyword(s):  
Power Series ◽  
Second Order ◽  
Euler Polynomials ◽  
Euler Numbers ◽  
Non Linear ◽  
Combinatorial Methods

In this paper, we first introduce a new second-order non-linear recursive polynomials U h , i ( x ) , and then use these recursive polynomials, the properties of the power series and the combinatorial methods to prove some identities involving the Fubini polynomials, Euler polynomials and Euler numbers.

scholarly journals Some extensions of the Prabhu-Srivastava theorem involving the (p,q)-gamma function

Filomat ◽  
2017 ◽  
Vol 31 (14) ◽  
pp. 4507-4513
Author(s):  
Ji-Cai Liu ◽  
Jichun Liu
Keyword(s):  
Gamma Function ◽  
Digamma Function ◽  
Derivatives Of

In this paper, we obtain some limit formulas for derivatives of (p,q)-gamma function and (p,q)- digamma function at their poles. These limit formulas extend the Prabhu-Srivastava theorem involving gamma function and digamma function.

scholarly journals A note on characteristic function for Bernstein polynomials involving special numbers and polynomials

Filomat ◽  
2020 ◽  
Vol 34 (2) ◽  
pp. 543-549
Author(s):  
Buket Simsek
Keyword(s):  
Characteristic Function ◽  
Binomial Distribution ◽  
Bernstein Polynomials ◽  
Random Variable ◽  
Stirling Numbers ◽  
Bernoulli Numbers ◽  
Discrete Random Variable ◽  
Euler Numbers ◽  
Negative Order ◽  
Special Numbers And Polynomials

The aim of this present paper is to establish and study generating function associated with a characteristic function for the Bernstein polynomials. By this function, we derive many identities, relations and formulas relevant to moments of discrete random variable for the Bernstein polynomials (binomial distribution), Bernoulli numbers of negative order, Euler numbers of negative order and the Stirling numbers.

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