An Introduction to Combinatory Analysis
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Since this is an identity we may multiply out the left-hand side and equate the coefficients of the successive powers oi y to zero; obtaining Jh — «i = 0, h^ — ajix + a2 = 0, ^3 — «! 7^2 + a-2 hi — «. J = 0, hn - ajin-i + aiK-i - ... + {-y-an = 0, hn + 2 - CllK-vi + a^hn - ... + {-Tanh = 0, relations which enable us to express any function ^, „ in terms of members of the series ai, a^, ag, ... «».
7. In the applications to combinatory analysis it usually happens that we may regard n as being in...definitely great and then the relations are simply hi — Oi = 0, ^2 - «! Ai + a. 2 - 0, hs — ajh + a^hi — a-i-O, continued indefinitely.
The before-written identity now becomes (1 — a^y + a^y" - a^y^ + ... Ad inf. ) (1 + hiy + h^y" + h^y^ + ... Ad inf. ) s 1, and herein writing —y for y and transposing the factors we find (1 - hiy + h^y^ - hsy^ + ... Ad inf. ) (1 + a^y + a-^y"^ + a-i'if + ... Ad inf. ) = 1, an identity which is derivable from the former by interchange of the symbols a and h.
What to read after An Introduction to Combinatory Analysis?
You can find similar books in the "Read Also" column, or choose other free books by Percy Alexander Macmahon to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
Since this is an identity we may multiply out the left-hand side and equate the coefficients of the successive powers oi y to zero; obtaining Jh — «i = 0, h^ — ajix + a2 = 0, ^3 — «! 7^2 + a-2 hi — «. J = 0, hn - ajin-i + aiK-i - ... + {-y-an = 0, hn + 2 - CllK-vi + a^hn - ... + {-Tanh = 0, relations which enable us to express any function ^, „ in terms of members of the series ai, a^, ag, ... «».
7. In the applications to combinatory analysis it usually happens that we may regard n as being in...definitely great and then the relations are simply hi — Oi = 0, ^2 - «! Ai + a. 2 - 0, hs — ajh + a^hi — a-i-O, continued indefinitely.
The before-written identity now becomes (1 — a^y + a^y" - a^y^ + ... Ad inf. ) (1 + hiy + h^y" + h^y^ + ... Ad inf. ) s 1, and herein writing —y for y and transposing the factors we find (1 - hiy + h^y^ - hsy^ + ... Ad inf. ) (1 + a^y + a-^y"^ + a-i'if + ... Ad inf. ) = 1, an identity which is derivable from the former by interchange of the symbols a and h.
What to read after An Introduction to Combinatory Analysis?
You can find similar books in the "Read Also" column, or choose other free books by Percy Alexander Macmahon to read onlineMoreLess
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