The chord‐length distribution function [γ′′(r )] of any bounded polyhedron has a closed analytic expression which changes in the different subdomains of the r range. In each of these, the γ′′(r ) expression only involves, as transcendental contributions, inverse trigonometric functions of argument equal to R [r , Δ₁], Δ₁ being the square root of a second‐degree r polynomial and R [x , y ] a rational function. As r approaches δ, one of the two end points of an r subdomain, the derivative of γ′′(r ) can only show singularities of the forms |r − δ|⁻ⁿ and |r − δ|^{−m +1/2}, with n and m appropriate positive integers. Finally, the explicit analytic expressions of the primitives are also reported.

中文翻译：

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多面体的弦长分布。

任何有界多面体的弦长分布函数[γ''（r）]具有一个封闭的解析表达式，该表达式在r范围的不同子域中发生变化。在每个这些，γ''（ [R ）的表达仅涉及，作为先验贡献，逆参数的三角函数等于- [R [ - [R，Δ ₁ ]，Δ ₁是第二度的平方根ř多项式和ř [ x，  y ]有理函数。当r接近δ时，r子域的两个端点之一即γ''（r）仅能显示形式的奇异| r -δ| ^{− n}和| r -δ| ^{− m +1/2}，其中n和m为适当的正整数。最后，还报告了基元的显式解析表达式。