a x + y i = ∑ n = 0 ∞ ( ∫ 1 a x t d t ) n n ! ( ∑ n = 0 ∞ ( − 1 ) n ( ∫ 1 a y t d t ) 2 n ( 2 n ) ! + i ∑ n = 0 ∞ ( − 1 ) n ( ∫ 1 a y t d t ) 2 n + 1 ( 2 n + 1 ) ! ) {\displaystyle a^{x+yi}=\sum _{n=0}^{\infty }{\frac {\left(\int _{1}^{a}\!{\frac {x}{t}}\,dt\,\right)^{n}}{n!}}\left(\sum _{n=0}^{\infty }{\frac {(-1)^{n}\left(\int _{1}^{a}\!{\frac {y}{t}}\,dt\,\right)^{2n}}{(2n)!}}+i\sum _{n=0}^{\infty }{\frac {(-1)^{n}\left(\int _{1}^{a}\!{\frac {y}{t}}\,dt\,\right)^{2n+1}}{(2n+1)!}}\right)}
