Abstract
S. Ramanujan introduced a technique, known as Ramanujan’s Master Theorem, which provides an explicit expression for the Mellin transform of a function in terms of the analytic continuation of its Taylor coefficients. The history and proof of this result are reviewed, and a variety of applications is presented. Finally, a multi-dimensional extension of Ramanujan’s Master Theorem is discussed.
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O. Espinosa is deceased.
The fifth author wishes to thank the partial support of NSF-DMS 0070757. The work of the last author was partially supported, as a graduate student, by the same grant.
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Amdeberhan, T., Espinosa, O., Gonzalez, I. et al. Ramanujan’s Master Theorem. Ramanujan J 29, 103–120 (2012). https://doi.org/10.1007/s11139-011-9333-y
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DOI: https://doi.org/10.1007/s11139-011-9333-y
Keywords
- Integrals
- Analytic continuation
- Series representation
- Hypergeometric functions
- Random walk integrals
- Method of brackets