Document Type : Research Paper
1 Department of Mathematics, Faculty of Mathematical Sciences, University for Development Studies, Ghana
2 Department of Mathematics, College of Arts and Science-Wadi Aldawaser, 11991, Prince Sattam bin Abdulaziz University, Alkharj, Kingdom of Saudi Arabia
3 Government College Jodhpur, JNV University Jodhpur, Rajasthan, India
Motivated by the $k$-digamma function, we introduce a $k$-extension of the Nielsen's $\beta$-function, and further study some properties and inequalities of the new function.