例如:A(x)=1+2*x+19*x^2/2!+375*x^3/3!+11597*x^4/4!+494073*x^5/5!+26973213*x^6/6!+1802125335*x^7/7!+142754111145*x^8/8!+13101722399345*x^9/9!+1369021004761137*x^10/10!+160654614141341015*x^11/11!+20941910928902384125*x ^12/12!+3005307338361684404233*x ^13/13!+471283774693207248796085*x ^14/14!+8025730837733916859891447*x^15/15!+。。。
满足
exp(A(x))=1+exp(x*A(xexp(3^2*x*A(x))/3!+exp(4^2*x*A(x))/4!+exp(5^2*x*A(x))/5!+exp(6^2*x*A(x))/6!+exp(7^2*x*A(x))/7!+exp(8^2*x*A(x))/8!+。。。
相关系列。
exp(A(x)-1)=1+2*x+23*x^2/2!+497*x^3/3!+16152*x ^4/4!+708675*x ^ 5/5!+39396793*x ^6/6!+2661970792*x ^ 7/7!+212306874267*x^8/8!+19558829912359*x ^9/9!+2047036462062752*x^10/10!+。。。