ESF - The Encyclopedia of Special Functions

About Equation LI2.2.1.1.1

$\begin{equation*} \begin{split} & \operatorname{dilog} (x)\approx (x - 1) \Biggl(-\frac{5}{4} + \frac{x}{4} - \frac{(x - 1)^{2}}{9} + \frac{(x - 1)^{3}}{16} - \frac{(x - 1)^{4}}{25} + \frac{(x - 1)^{5}}{36} - \\ & \quad{}\quad{}\frac{(x - 1)^{6}}{49} + \frac{(x - 1)^{7}}{64} - \frac{(x - 1)^{8}}{81} + \frac{(x - 1)^{9}}{100} - \frac{(x - 1)^{10}}{121} + \frac{(x - 1)^{11}}{144} - \\ & \quad{}\quad{}\frac{(x - 1)^{12}}{169} + \frac{(x - 1)^{13}}{196} - \frac{(x - 1)^{14}}{225} + \frac{(x - 1)^{15}}{256}\ldots\Biggr) \end{split} \end{equation*}$

Absolute reference: LI2:asympt:1:terms

LaTeX encoding

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\operatorname{dilog} (x)\approx (x - 1) \Biggl(-\frac{5}{4} + \frac{x}{4} - \frac{(x - 1)^{2}}{9} + \frac{(x - 1)^{3}}{16} - \frac{(x - 1)^{4}}{25} + \frac{(x - 1)^{5}}{36} - \\ \quad{}\quad{}\frac{(x - 1)^{6}}{49} + \frac{(x - 1)^{7}}{64} - \frac{(x - 1)^{8}}{81} + \frac{(x - 1)^{9}}{100} - \frac{(x - 1)^{10}}{121} + \frac{(x - 1)^{11}}{144} - \\ \quad{}\quad{}\frac{(x - 1)^{12}}{169} + \frac{(x - 1)^{13}}{196} - \frac{(x - 1)^{14}}{225} + \frac{(x - 1)^{15}}{256}\ldots\Biggr)

Maple encoding

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`&sepsequence`(`&nothing`,`&operatorname`(dilog)(x),approx,nullspace,(x-1)*`&delimiter`(leftparens,rightparens,false,`&sepsequence`(`&nothing`,-5/4+1/4*x-1/9*(x-1)^2+1/16*(x-1)^3-1/25*(x-1)^4+1/36*(x-1)^5-1/49*(x-1)^6+1/64*(x-1)^7-1/81*(x-1)^8+1/100*(x-1)^9-1/121*(x-1)^10+1/144*(x-1)^11-1/169*(x-1)^12+1/196*(x-1)^13-1/225*(x-1)^14+1/256*(x-1)^15,ldots)))