组织结构:A(x)=1+x+7*x^2+97*x^3+1987*x*4+53281*x^5+1754245*x^6+68228209*x^7+3055471369*x^8+154724090845*x^9+8740256396563*x^10+。。。
定义说明。
exp(n^2*积分A(x)dx)/A(x)中x^k的系数表开始于:
n=0:[1,-1,-6,-84,-1764,-48360,-1620186,-63857556,…];
n=1:[1,0,-6,-88,-1830,-249144/5,-1661842,-2284994352/35,…];
n=2:[1,3,0,-90,-2025,-272391/5,-896968/5,-488439972/7,…];
n=3:[1,8,30,0,-2100,-31856/5,-10175418/5,-545952984/7,…];
n=4:[1,15,114,532,0,-327564/5,-2389194,-3186733572/35,…];
n=5:[1,24,294,2416,13536,0,-2539746,-763395912/7,…];
n=6:[1,351624,7542,68415,2234001/5,0,-4102900932/35,…];
n=7:[1,48,1170,19320,242550,12134424/5,90334582/5,0,…]。。。
其中主对角线在初始项后全部为零,说明当n>0时,0=[x^n]exp(n^2*积分A(x)dx)/A(x)。
相关系列。
exp(积分A(x)dx)=1+x+2*x^2/2!+18*x^3/3!+648*x^4/4!+50904*x^5/5!+6700464*x ^6/6!+1310200848*x^7/7!+354395417472*x ^8/8!+126396068810112*x ^ 9/9!+。。。
A’(x)/A(x)=1+13*x+271*x ^2+7489*x ^3+253771*x ^4+10113877*x ^5+461995381*x ^6+23766009457*x ^7+1359214691545*x ^8+85572483605593*x ^9+。。。
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