## Serial relations and symbolic calculus |

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1+Ao able to expand able to find approximate values arbitrary constant arbitrary quantity asymptotic series basal function becomes Bernoulli Polynomial calculation Cn{u coefficients complete solution connexion consequently consider corresponding d"y0 xn definite integrals Differential Series dny0 dnz0 doubly infinite series equivalent Evidently finite following transformations formula fractional differentiation Further gamma-function Gaussian differential equation generatrix function Hence with regard identical infer known function left-hand side Legendre's equation Likewise line from bottom linear differential equation ln(l lower limit mathematical obviously p(Ti p(Ti+<on particular solution periodic functions polynomial positive integer positive whole number power series problem readily derive readily obtain recurrent relation reference replace right-hand member right-hand side serial relation series 20a shown simple infinite series Substituting summation Symbolic Calculus tion valid whence we obtain whereas write y=ex yields zero