Hypergeometric functions in one variable

This is a Fuchsian equation of order n with singularities at 0, 1,∞. The local exponents read, 1− β1, . . . , 1− βn at z = 0 α1, . . . , αn at z =∞ 0, 1, . . . , n− 2, −1 + ∑n 1 (βi − αi) at z = 1 When the βi are distinct modulo 1 a basis of solutions at z = 0 is given by the functions z1−βi nFn−1 ( α1 − βi + 1, . . . , αn − βi + 1 β1 − βi + 1, ..∨.., βn − βi + 1 ∣∣∣∣ z) (i = 1, . . . , n). Here ..∨.. denotes suppression of the term βi − βi + 1 and nFn−1 stands for the generalised hypergeometric function in one variable