| dbo:abstract |
En mathématiques, le « master theorem » de Ramanujan (littéralement, « théorème maître », dû à Srinivasa Ramanujan, et trouvé dans ses carnets après sa mort) est une technique produisant une forme explicite de la transformée de Mellin d'une fonction analytique. (fr) In mathematics, Ramanujan's Master Theorem, named after Srinivasa Ramanujan, is a technique that provides an analytic expression for the Mellin transform of an analytic function. The result is stated as follows: If a complex-valued function has an expansion of the form then the Mellin transform of is given by where is the gamma function. It was widely used by Ramanujan to calculate definite integrals and infinite series. Higher-dimensional versions of this theorem also appear in quantum physics (through Feynman diagrams). A similar result was also obtained by Glaisher. (en) |
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| rdfs:comment |
En mathématiques, le « master theorem » de Ramanujan (littéralement, « théorème maître », dû à Srinivasa Ramanujan, et trouvé dans ses carnets après sa mort) est une technique produisant une forme explicite de la transformée de Mellin d'une fonction analytique. (fr) In mathematics, Ramanujan's Master Theorem, named after Srinivasa Ramanujan, is a technique that provides an analytic expression for the Mellin transform of an analytic function. The result is stated as follows: If a complex-valued function has an expansion of the form then the Mellin transform of is given by where is the gamma function. It was widely used by Ramanujan to calculate definite integrals and infinite series. Higher-dimensional versions of this theorem also appear in quantum physics (through Feynman diagrams). A similar result was also obtained by Glaisher. (en) |
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Master theorem de Ramanujan (fr) Ramanujan's master theorem (en) |
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