Generalized Bessel Function Distributions

Abstract

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Efficient Computation of the Special Cases of the Generalized Bessel Function Distributions

“…These special cases are important because they cover cases that were not discussed in either Progri 2016 [1] and Progri 2018 [2]. There was a provision made in Progri 2016 [1] and an attempt to derive the main special case which is the one corresponding to the integer values of . However, the derivations in Progri 2016 [1] were not complete.…”

“…There was a provision made in Progri 2016 [1] and an attempt to derive the main special case which is the one corresponding to the integer values of . However, the derivations in Progri 2016 [1] were not complete. Hence, the main focus on this journal paper is to derive this closed form expression of the [1]- [16]) and in some cases the of Srivastava's triple hypergeometric series (3) [ , , ] ii [18]- [22] in MATLAB.…”

“…However, the derivations in Progri 2016 [1] were not complete. Hence, the main focus on this journal paper is to derive this closed form expression of the [1]- [16]) and in some cases the of Srivastava's triple hypergeometric series (3) [ , , ] ii [18]- [22] in MATLAB. Back in 2016 I was barely understanding the Kampé de Fériet function (or double hypergeometric series [1]- [16]) and I made an unsuccessful attempt to derive an inefficient implementation of the Srivastava's triple hypergeometric series (3) [ , , ] [18]- [22] which luckily I did not publish.…”

“…Hence, the main focus on this journal paper is to derive this closed form expression of the [1]- [16]) and in some cases the of Srivastava's triple hypergeometric series (3) [ , , ] ii [18]- [22] in MATLAB. Back in 2016 I was barely understanding the Kampé de Fériet function (or double hypergeometric series [1]- [16]) and I made an unsuccessful attempt to derive an inefficient implementation of the Srivastava's triple hypergeometric series (3) [ , , ] [18]- [22] which luckily I did not publish. This limitation in the computational capability was filled in 2018 with the arrival of the Progri 2018 [2] where I developed a profoundly improved implementation in MATLAB of the Kampé de Fériet function (or double hypergeometric series [1]- [16]).…”

“…Back in 2016 I was barely understanding the Kampé de Fériet function (or double hypergeometric series [1]- [16]) and I made an unsuccessful attempt to derive an inefficient implementation of the Srivastava's triple hypergeometric series (3) [ , , ] [18]- [22] which luckily I did not publish. This limitation in the computational capability was filled in 2018 with the arrival of the Progri 2018 [2] where I developed a profoundly improved implementation in MATLAB of the Kampé de Fériet function (or double hypergeometric series [1]- [16]). Moreover, this limitation in the computational capability was entirely eliminated in 2019 as discussed in Appendices A through F in this paper.…”