New extension of beta, Gauss and confluent hypergeometric functions

• الحاوية / القاعدة: Cumhuriyet Science Journal
• المؤلفون الرئيسيون: Umar Muhammad Abubakar, Muhammad Lawan Kaurangini
• التنسيق: مقال
• اللغة: الإنجليزية
• منشور في: Sivas Cumhuriyet Üniversitesi 2021-09-01
• الموضوعات: gamma function; beta function; beta distribution; pochhammer symbol; mellin transform
• الوصول للمادة أونلاين: https://dergipark.org.tr/en/download/article-file/1448515
• تدمد: 2587-2680

There are many extensions and generalizations of Gamma and Beta functions in the literature. However, a new extension of the extended Beta function B_(ζ〖, α〗_1)^(α_2;〖 m〗_1,〖 m〗_2 ) (a_1,a_2 ) was introduced and presented here because of its important properties. The new extended Beta function has symmetric property, integral representations, Mellin transform, inverse Mellin transform and statistical properties like Beta distribution, mean, variance, moment and cumulative distribution which ware also presented. Finally, the new extended Gauss and Confluent Hypergeometric functions with their propertied were introduced and presented.