例如:D(x)=1+x^2/2!+6*x^4/4!+114*x^6/6!+4224*x^8/8!+258696*x ^10/10!+23685696*x ^12/12!+3030422544*x ^ 14/14!+516368179584*x ^16/16!+113039478326016*x ^18/18!+。。。
和相关系列
S(x)=x+3*x^3/3!+39*x^5/5!+1137*x^7/7!+58221*x^9/9!+4615623*x ^11/11!+523484019*x^13/13!+80413567317*x ^ 15/15!+16072230046041*x ^17/17!+4053246141598443*x ^19/19!+。。。
C(x)=1+x^2/2!+9*x^4/4!+189*x^6/6!+7521*x^8/8!+487521*x^10/10!+46747449*x ^12/12!+6218441469*x ^14/14!+1095843999681*x ^16/16!+247107215918241*x^18/18!+。。。
满足
C(x)^2-S(x)*^2=1,
3*C(x)^2-2*D(x)^3=1。
相关扩展。
C(x)^2=1+2*x^2/2!+24*x^4/4!+648*x^6/6!+31296*x^8/8!+2366352*x ^10/10!+257865984*x^12/12!+3826641488*x^14/14!+7419295374336*x ^16/16!+1820980419409152*x ^18/18!+。。。
D(x)^2=1+2*x^2/2!+18*x^4/4!+408*x^6/6!+17352*x ^8/8!+1184832*x ^10/10!+118618128*x ^12/12!+16371203328*x^14/14!+2979295540992*x ^16/16!+691248148134912*x ^18/18!+。。。
D(x)^3=1+3*x^2/2!+36*x^4/4!+972*x^6/6!+46944*x^8/8!+3549528*x^10/10!+386798976*x^12/12!+57399622272*x^14/14!+11128943061504*x ^16/16!+2731470629113728*x^18/18!+。。。
这样2*D(x)^3-3*S(x)*2=2。
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