Expressions of the Laguerre polynomial and some other special functions in terms of the generalized Meijer \(G\)-functions. (English) Zbl 1510.33015
Summary: We investigate the relation of generalized Meijer \(G \)-functions with some other special functions. We prove the generalized form of Laguerre polynomials, product of Laguerre polynomials with exponential functions, logarithmic functions in terms of generalized Meijer \(G \)-functions. The generalized confluent hypergeometric functions and generalized tricomi confluent hypergeometric functions are also expressed in terms of the generalized Meijer \(G \)-functions.
MSC:
| 33C60 | Hypergeometric integrals and functions defined by them (\(E\), \(G\), \(H\) and \(I\) functions) |
| 33C10 | Bessel and Airy functions, cylinder functions, \({}_0F_1\) |
| 45P05 | Integral operators |
Keywords:
Meijer \(G\)-function; generalized Meijer \(G\)-function; Laguerre polynomial; hypergeometric function; confluent hypergeometric functionSoftware:
DLMFReferences:
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