| Budget Amount *help |
¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000)
Fiscal Year 2017: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2016: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2015: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2014: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
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| Outline of Final Research Achievements |
We say that a function is differentially transcendental when it does not satisfy any algebraic differential equation. There are various studies on differential transcendence of functions satisfying difference equations. O. Hoelder's study on Gamma function is typical. In 1905, H. Tietze studied differential transcendence of solutions of difference Riccati equations, and obtained a sufficient condition. In this study, H. Tietze's result is made purely algebraic, and applicable to difference Riccati equations with other transforming operators such as one of q-difference, Mahler type, etc. As an application, it is seen that a solution of q-Airy equation is differentially transcendental when q is not a root of unity. The theory and the method for proving irreducibility of q-Painleve euqations are found to be applicable to a d-Painleve equation.
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