Concepts inREDUCE package for the indefinite and definite summation
Summation
Summation is the operation of adding a sequence of numbers; the result is their sum or total. If numbers are added sequentially from left to right, any intermediate result is a partial sum, prefix sum, or running total of the summation. The numbers to be summed (called addends, or sometimes summands) may be integers, rational numbers, real numbers, or complex numbers.
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Bill Gosper
Ralph William Gosper, Jr. (born 1943), known as Bill Gosper, is an American mathematician and programmer from Pennsauken Township, New Jersey. Along with Richard Greenblatt, he may be considered to have founded the hacker community, and holds a place of pride in the Lisp community.
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Pochhammer symbol
In mathematics, the Pochhammer symbol introduced by Leo August Pochhammer is the notation (x)n, where n is a non-negative integer. Depending on the context the Pochhammer symbol may represent either the rising factorial or the falling factorial as defined below. Care needs to be taken to check which interpretation is being used in any particular article. Pochhammer himself actually used (x)n with yet another meaning, namely to denote the binomial coefficient .
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Wilf¿Zeilberger pair
In mathematics, specifically combinatorics, a Wilf¿Zeilberger pair, or WZ pair, is a pair of functions that can be used to certify certain combinatorial identities. In particular, WZ pairs are instrumental in the evaluation of many sums involving binomial coefficients, factorials, and in general any hypergeometric series. A function's WZ counterpart may be used to find an equivalent, and much simpler sum.
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Doron Zeilberger
Doron Zeilberger (¿¿¿¿¿ ¿¿¿¿¿¿¿¿, born 2 July 1950 in Haifa, Israel) is an Israeli mathematician, known for his work in combinatorics. He is a Board of Governors Professor of Mathematics at Rutgers University. He received his doctorate from the Weizmann Institute of Science in 1976, under the direction of Harry Dym. Zeilberger has made numerous important contributions to combinatorics, hypergeometric identities, and q-series.
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Binomial coefficient
In mathematics, binomial coefficients are a family of positive integers that occur as coefficients in the binomial theorem. They are indexed by two nonnegative integers; the binomial coefficient indexed by n and k is usually written, and it is the coefficient of the x term in the polynomial expansion of the binomial power (1 + x). Arranging binomial coefficients into rows for successive values of n, and in which k ranges from 0 to n, gives a triangular array called Pascal's triangle.
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Factorial
The first few and selected larger members of the sequence of factorials. The values specified in scientific notation are rounded to the displayed precision. In mathematics, the factorial of a non-negative integer n, denoted by n!, is the product of all positive integers less than or equal to n. For example, The value of 0! is 1, according to the convention for an empty product.
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Rational function
In mathematics, a rational function is any function which can be written as the ratio of two polynomial functions. Neither the coefficients of the polynomials nor the values taken by the function are necessarily rational numbers.
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