形式为 a n + 1 =pa n + s/qa n + r , p,q,r,s ∈ R的线性分式递推数列是高中数学数列部分常见题型。本文从初等数学的角度:化归思想,取倒数,转化等差(或等比)数列,给出形式为a n + 1 =pa n + s/qa n + r的线性分式递推数列的通项公式...形式为 a n + 1 =pa n + s/qa n + r , p,q,r,s ∈ R的线性分式递推数列是高中数学数列部分常见题型。本文从初等数学的角度:化归思想,取倒数,转化等差(或等比)数列,给出形式为a n + 1 =pa n + s/qa n + r的线性分式递推数列的通项公式及周期存在的判定,并举例说明其价值。展开更多
Fully normalized associated Legendre functions(fnALFs)are a set of orthogonal basis functions that are usually calculated by using the recurrence equation.This paper presented the applicability and universality of the...Fully normalized associated Legendre functions(fnALFs)are a set of orthogonal basis functions that are usually calculated by using the recurrence equation.This paper presented the applicability and universality of the standard forward column/row recurrence equation based on the isolated singular factor method and extended-range arithmetic.Isolating a singular factor is a special normalization method that can improve the universality of the standard forward row recurrence equation to a certain extent,its universality can up to degree hundreds.However,it is invalid for standard forward column recurrence equation.The extended-range arithmetic expands the double-precision number field to the quad-precision numberfield.The quad-precision numberfield can retain more significant digits in the operation process and express larger and smaller numbers.The extended-range arithmetic can significantly improve the applicability and universality of the standard forward column/row recurrence equations,its universality can up to degree several thousand.However,the quad-precision numberfield operation needs to occupy more storage space,which is why its operation speed is slow and undesirable in practical applications.In this paper,the X-number method is introduced in the standard forward row recurrence equation for thefirst time.With the use of the X-number method,fnALFs can be recursed to 4.2 billion degree by using standard forward column/row recurrence equations.展开更多
文摘形式为 a n + 1 =pa n + s/qa n + r , p,q,r,s ∈ R的线性分式递推数列是高中数学数列部分常见题型。本文从初等数学的角度:化归思想,取倒数,转化等差(或等比)数列,给出形式为a n + 1 =pa n + s/qa n + r的线性分式递推数列的通项公式及周期存在的判定,并举例说明其价值。
文摘Fully normalized associated Legendre functions(fnALFs)are a set of orthogonal basis functions that are usually calculated by using the recurrence equation.This paper presented the applicability and universality of the standard forward column/row recurrence equation based on the isolated singular factor method and extended-range arithmetic.Isolating a singular factor is a special normalization method that can improve the universality of the standard forward row recurrence equation to a certain extent,its universality can up to degree hundreds.However,it is invalid for standard forward column recurrence equation.The extended-range arithmetic expands the double-precision number field to the quad-precision numberfield.The quad-precision numberfield can retain more significant digits in the operation process and express larger and smaller numbers.The extended-range arithmetic can significantly improve the applicability and universality of the standard forward column/row recurrence equations,its universality can up to degree several thousand.However,the quad-precision numberfield operation needs to occupy more storage space,which is why its operation speed is slow and undesirable in practical applications.In this paper,the X-number method is introduced in the standard forward row recurrence equation for thefirst time.With the use of the X-number method,fnALFs can be recursed to 4.2 billion degree by using standard forward column/row recurrence equations.
