Abstract
The hypergeometric series is an extension of the geometric series. The confluent hypergeometric function is the solution of the hypergeometric differential equation [θ(θ +b−1)−z(θ +a)]w = 0. Kummer’s first formula and Kummer’s second formula are of significant importance in solving the hypergeometric differential equations. Kummer has developed six solutions for the differential equation and twenty connecting formulas during the period of 1865-1866. Each connecting formula consist of a solution expressed as the combination of two other solutions. Recently in 2021, these solutions were extensively used by Schweizer [13] in practical problems specially in Physics. Here we extend the connecting formulas obtained by Kummer to obtain the other six solutions w1(z), w2(z), w3(z), w4(z), w5(z) and w6(z) as the combination of three solutions.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
