나무 그래프: 두 판 사이의 차이
내용 삭제됨 내용 추가됨
126번째 줄:
f(x)&=\sum_{k\in M} {{x^{|k|}}\over{|k|!}} {{|k|!}\over{\prod_{n=1}^\infty (n!)^{k_n} k_n!}} \prod_{n=1}^\infty (T_n)^{k_n}\\
&=\sum_{k\in M} {{|k|!}\over{|k|!}} {{x^{|k|} { \prod_{n=1}^\infty (T_n)^{k_n}}}\over{\prod_{n=1}^\infty (n!)^{k_n} {k_n!}}} \\
&=\sum_{k\in M} {x^{|k|}} \prod_{n=1}^\infty\left({{T_n}\over{n!}}\right)^{k_n} {{1}\over{k_n!}} \\
&=\sum_{k\in M} {x^{\sum_{n=1}^\infty nk_n}} \prod_{n=1}^\infty\left({{T_n}\over{n!}}\right)^{k_n} {{1}\over{k_n!}} \\
&=\sum_{k\in M} \prod_{n=1}^{\infty}{x_{n}^{k_n}} \prod_{n=1}^\infty\left({{T_n}\over{n!}}\right)^{k_n} {{1}\over{k_n!}} \\
&= \sum_{k\in M} \prod_{n=1}^\infty\left({{T_nx_n}\over{n!}}\right)^{k_n} {{1}\over{k_n!}} \\
& =\prod_{n=1}^\infty\sum_{k_n=0}^\infty\left({{T_nx_n}\over{n!}}\right)^{k_n} {{1}\over{k_n!}} \\
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