| Budget Amount *help |
¥11,440,000 (Direct Cost: ¥8,800,000、Indirect Cost: ¥2,640,000)
Fiscal Year 2015: ¥2,860,000 (Direct Cost: ¥2,200,000、Indirect Cost: ¥660,000)
Fiscal Year 2014: ¥2,860,000 (Direct Cost: ¥2,200,000、Indirect Cost: ¥660,000)
Fiscal Year 2013: ¥2,860,000 (Direct Cost: ¥2,200,000、Indirect Cost: ¥660,000)
Fiscal Year 2012: ¥2,860,000 (Direct Cost: ¥2,200,000、Indirect Cost: ¥660,000)
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| Outline of Final Research Achievements |
We calculated explicitly the circuit matrices associated with Gauss' {}_2F1, the generalized hypergeometric functions {}_{n+1}F_n, Apell's F_1, F_2, F_3, Jordan-Pochhammer F_{JP}, and Lauricella's F_D, and, by using them, we determine the conditionｓ that the corresponding (system of) diffferential equations being irreducible. On the other hand, in the cases of F_2, F_3, F_4, we study the contiguity relations and give the conditionｓ that the corresponding systemｓ being reducible.
We prove that, in each case of the classical hypergeometric equations and Gelfand's hypergeometric system on the space of point configurations, the integral of a multivalued functions over any cycle satisfies the system of differential equations. Here the classical hypergeometric equations mean the equations satisfied by Appell's F_1, F_2, F_3, F_4, Lauricella's F_D, F_A, F_B, F_C, and the generalized hypergeometric function {}_{n+1}F_n.
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