不定代数积分的两项递推公式
Two-term recurrence formulae for indefinite algebraic integrals
摘要：
为涉及${P_2}^n$、${P_3}^n$、${P_4}^n$、${P_1}^m {Q_1}^n$、$E_1 {P_1}^n$、${P_1}^m {Q_2}^n$、$E_1 {P_2}^n$、${P_2}^m {Q_2}^n$、${P_1}^m {Q_1}^n {S_1}^p$、$E_1 {P_1}^m {Q_1}^n$、${P_1}^m {Q_1}^n {S_2}^p$和${P_1}^m {Q_1}^n {S_1}^p {T_1}^q$类型的因子的函数的不定积分提供了两项递归关系，其中$P_i$、$Q_j$、$S_k$和$T_l$表示任意次数的多项式$i$、$j$、$k$和$l$，$E_1$表示该变量中的任意线性多项式的指数函数，并且$m$、$n$、$p$和$q$是任意常数指数。这136个关系式保持被积函数的形式不变，并以单位的步骤递增或递减指数。
英文摘要：
Two-term recurrence relations are supplied for indefinite integrals of functions that involve factors of the types ${P_2}^n$, ${P_3}^n$, ${P_4}^n$, ${P_1}^m {Q_1}^n$, $E_1 {P_1}^n$, ${P_1}^m {Q_2}^n$, $E_1 {P_2}^n$, ${P_2}^m {Q_2}^n$, ${P_1}^m {Q_1}^n {S_1}^p$, $E_1 {P_1}^m {Q_1}^n$, ${P_1}^m {Q_1}^n {S_2}^p$, and ${P_1}^m {Q_1}^n {S_1}^p {T_1}^q$, where $P_i$, $Q_j$, $S_k$ and $T_l$ denote arbitrary polynomials of degree $i$, $j$, $k$ and $l$ in the integration variable, $E_1$ represents the exponential function of an arbitrary linear polynomial in this variable, and $m$, $n$, $p$ and $q$ are arbitrary constant exponents. The 136 relations leave the form of an integrand unchanged and increment or decrement the exponents in steps of unity.
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