A Connection Formula for the q-Confluent Hypergeometric Function

作者：Morita Takeshi^*

来源：Symmetry Integrability and Geometry-Methods and Applications, 2013, 9: 050.

DOI：10.3842/SIGMA.2013.050

• q-Borel-Laplace transformation
• q-difference equation
• connection problem
• q-confluent hypergeometric function

We show a connection formula for the q-confluent hypergeometric functions 2 phi 1 (a, b; 0; q, x). Combining our connection formula with Zhang's connection formula for 2 phi 0 (a, b; -; q, x), we obtain the connection formula for the q-confluent hypergeometric equation in the matrix form. Also we obtain the connection formula of Kummer's confluent hypergeometric functions by taking the limit q -> 1(-) of our connection formula.

• 出版日期2013