| Budget Amount *help |
¥5,200,000 (Direct Cost: ¥4,000,000、Indirect Cost: ¥1,200,000)
Fiscal Year 2016: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2015: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2014: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2013: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2012: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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| Outline of Final Research Achievements |
Through this research project, the relation between the eigenfunctions of p-Laplacian and fundamental concepts of number theory, such as elliptic integral, elliptic function, hypergeometric function, arithmetic-geometric mean, etc., has come to be seen. We gave generalization of Jacobi elliptic function and the complete elliptic integral by generalized trigonometric functions, and as their application we presented Gauss-Legendre's type algorithm on the constant pi and generalization and expressions of solutions for classical differential equations. Regarding these series of results, we have received certain evaluations from P. Lindqvist, R. Manasevich, and M. Vuorinen, who are famous for research on p-Laplacian including generalized trigonometric functions, We believe that knowledge leading to cross-cutting research has been obtained.
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