Geodesic
Determinants of Elliptic Hypergeometric Integrals
Funkcionalʹnyj analiz i ego priloženiâ, Tome 43 (2009) no. 4, pp. 67-86

Voir la notice de l'article provenant de la source Math-Net.Ru

We start from an interpretation of the $BC_2$-symmetric “Type I” (elliptic Dixon) elliptic hypergeometric integral evaluation as a formula for a Casoratian of the elliptic hypergeometric equation and then generalize this construction to higher-dimensional integrals and higher-order hypergeometric functions. This allows us to prove the corresponding formulas for the elliptic beta integral and symmetry transformation in a new way, by proving that both sides satisfy the same difference equations and that these difference equations satisfy a needed Galois-theoretic condition ensuring the uniqueness of the simultaneous solution.
Keywords: elliptic hypergeometric function, difference equation, determinant, difference Galois theory. 
@article{FAA_2009_43_4_a5,
     author = {E. M. Rains and V. P. Spiridonov},
     title = {Determinants of {Elliptic} {Hypergeometric} {Integrals}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {67--86},
     publisher = {mathdoc},
     volume = {43},
     number = {4},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2009_43_4_a5/}
}
TY  - JOUR
AU  - E. M. Rains
AU  - V. P. Spiridonov
TI  - Determinants of Elliptic Hypergeometric Integrals
JO  - Funkcionalʹnyj analiz i ego priloženiâ
PY  - 2009
SP  - 67
EP  - 86
VL  - 43
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/FAA_2009_43_4_a5/
LA  - ru
ID  - FAA_2009_43_4_a5
ER  - 
%0 Journal Article
%A E. M. Rains
%A V. P. Spiridonov
%T Determinants of Elliptic Hypergeometric Integrals
%J Funkcionalʹnyj analiz i ego priloženiâ
%D 2009
%P 67-86
%V 43
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/FAA_2009_43_4_a5/
%G ru
%F FAA_2009_43_4_a5
E. M. Rains; V. P. Spiridonov. Determinants of Elliptic Hypergeometric Integrals. Funkcionalʹnyj analiz i ego priloženiâ, Tome 43 (2009) no. 4, pp. 67-86. http://geodesic.mathdoc.fr/item/FAA_2009_43_4_a5/