| Budget Amount *help |
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2018: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2017: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2016: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
|
|---|
| Outline of Final Research Achievements |
For generalized hypergeometric functions 3F2(1) we developed a general theory of contiguous relations. We established the linear independence of contiguous functions, existence and uniquness of contiguous relations, and algorithms for calculating their coefficients, as well as their group symmetry. As an application we constructed an infinite number of 3F2(1) continued fractions and determined exactly the leading asymptotics of their truncation errors. To do so we developed a discrete analogue of saddle point method for obtaining the asymptotic behavior of hypergeometric series containing a large parameter. As for Painleve equations we summarized the results obtained so far and set up the direction in which the next study should take. We also obtained some conditions for hypergeometric functions to admit gamma product formulas.
|
