| 000 | 02578nam a22004695i 4500 | ||
|---|---|---|---|
| 001 | 978-4-431-53938-4 | ||
| 003 | DE-He213 | ||
| 005 | 20140220083820.0 | ||
| 007 | cr nn 008mamaa | ||
| 008 | 110521s2011 ja | s |||| 0|eng d | ||
| 020 |
_a9784431539384 _9978-4-431-53938-4 |
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| 024 | 7 |
_a10.1007/978-4-431-53938-4 _2doi |
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| 050 | 4 | _aQA440-699 | |
| 072 | 7 |
_aPBM _2bicssc |
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| 072 | 7 |
_aMAT012000 _2bisacsh |
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| 082 | 0 | 4 |
_a516 _223 |
| 100 | 1 |
_aAomoto, Kazuhiko. _eauthor. |
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| 245 | 1 | 0 |
_aTheory of Hypergeometric Functions _h[electronic resource] / _cby Kazuhiko Aomoto, Michitake Kita. |
| 264 | 1 |
_aTokyo : _bSpringer Japan : _bImprint: Springer, _c2011. |
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| 300 |
_aXVI, 320 p. _bonline resource. |
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| 336 |
_atext _btxt _2rdacontent |
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| 337 |
_acomputer _bc _2rdamedia |
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| 338 |
_aonline resource _bcr _2rdacarrier |
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| 347 |
_atext file _bPDF _2rda |
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| 490 | 1 |
_aSpringer Monographs in Mathematics, _x1439-7382 |
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| 505 | 0 | _a1 Introduction: the Euler-Gauss Hypergeometric Function -- 2 Representation of Complex Integrals and Twisted de Rham Cohomologies -- 3 Hypergeometric functions over Grassmannians -- 4 Holonomic Difference Equations and Asymptotic Expansion References Index. | |
| 520 | _aThis book presents a geometric theory of complex analytic integrals representing hypergeometric functions of several variables. Starting from an integrand which is a product of powers of polynomials, integrals are explained, in an open affine space, as a pair of twisted de Rham cohomology and its dual over the coefficients of local system. It is shown that hypergeometric integrals generally satisfy a holonomic system of linear differential equations with respect to the coefficients of polynomials and also satisfy a holonomic system of linear difference equations with respect to the exponents. These are deduced from Grothendieck-Deligne’s rational de Rham cohomology on the one hand, and by multidimensional extension of Birkhoff’s classical theory on analytic difference equations on the other. | ||
| 650 | 0 | _aMathematics. | |
| 650 | 0 | _aFunctional analysis. | |
| 650 | 0 | _aGeometry. | |
| 650 | 1 | 4 | _aMathematics. |
| 650 | 2 | 4 | _aGeometry. |
| 650 | 2 | 4 | _aFunctional Analysis. |
| 700 | 1 |
_aKita, Michitake. _eauthor. |
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| 710 | 2 | _aSpringerLink (Online service) | |
| 773 | 0 | _tSpringer eBooks | |
| 776 | 0 | 8 |
_iPrinted edition: _z9784431539124 |
| 830 | 0 |
_aSpringer Monographs in Mathematics, _x1439-7382 |
|
| 856 | 4 | 0 | _uhttp://dx.doi.org/10.1007/978-4-431-53938-4 |
| 912 | _aZDB-2-SMA | ||
| 999 |
_c108809 _d108809 |
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