PageHeader : Funkcialaj Ekvacioj, 38 (1995) 243-266 Title : Connection Formulas for Appell's System $F_{4}$ Title : and Some Applications AuthorInfo : By AuthorInfo : Mitsuo KATO AuthorInfo : (Ryukyu University, Japan) section : Introduction section : 1. Preliminaries section : 2. Blowing up at $X=0$ , $\mathrm{Y}=1$ section : 3. Local solutions along $\{X_{2}=1\}$ section : 4. The local solutions along $\{X_{2}=0\}$ section : 5. Local solutions along $\{\mathrm{Y}_{0}=0\}$ section : 6. The connection formulas section : 7. A monodromy representation of $F_{4}$ section : 8. Reducible cases section : 9. Differential equations in reducible cases section : 10. The reducible cases and $F_{1}$ section : 11. The restriction of $(F_{4})$ to $C$ section : 12. The connection formulas among $\sigma_{i}$ , $\tau_{i}$ section : 13. The monodromy of the DEQ(4.1) section : 14. Reducible case of (4.1) section : References