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182
A telescoping method for double summations
 J. Comput. Appl. Math
"... We present a method to prove hypergeometric double summation identities. Given a hypergeometric term F(n,i,j), we aim to find a difference operator L = a0(n)N 0 + a1(n)N 1 + · · · + ar(n)N r and rational functions R1(n,i,j),R2(n,i,j) such that LF = ∆i(R1F) + ∆j(R2F). Based on simple divisibility c ..."
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Cited by 5 (2 self)
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We present a method to prove hypergeometric double summation identities. Given a hypergeometric term F(n,i,j), we aim to find a difference operator L = a0(n)N 0 + a1(n)N 1 + · · · + ar(n)N r and rational functions R1(n,i,j),R2(n,i,j) such that LF = ∆i(R1F) + ∆j(R2F). Based on simple divisibility
A Telescoping Algorithm for Double Summations
, 2005
"... We present an algorithm to prove hypergeometric double summation identities. Given a hypergeometric term F(n,i,j), we aim to find a difference operator L = a0(n)N 0 + a1(n)N 1 + · · · + ar(n)N r and rational functions R1(n,i,j),R2(n,i,j) such that LF = ∆i(R1F) + ∆j(R2F). Based on simple divisibili ..."
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We present an algorithm to prove hypergeometric double summation identities. Given a hypergeometric term F(n,i,j), we aim to find a difference operator L = a0(n)N 0 + a1(n)N 1 + · · · + ar(n)N r and rational functions R1(n,i,j),R2(n,i,j) such that LF = ∆i(R1F) + ∆j(R2F). Based on simple
1 On the relation between double summations and tetrahedral numbers
"... Abstract In this paper we provide an inverse proof of the relation between a particular class of double sums and tetrahedral numbers. Thus, we present a compact formula to reduce the number of calculations necessary to solve such a kind of problems. The initial identity is confirmed “a posteriori ” ..."
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” using the formula mentioned above. There exist different methods to solve summations [12] depending on the particular problem we are working on. In this brief paper, we explain that it’s possible to use a compact formula to minimize the calculations when we are involved in a particular class of double
On Some Transformation and Summation Formulas for the HFunction of two Variables
"... Abstract: In the present paper we establish four transformations of double infinite series involving the Hfunction of two variables. These formulas are then used to obtain double summation formulas for the Hfunction of two variables. Our results are quite general in character and a number of summa ..."
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Abstract: In the present paper we establish four transformations of double infinite series involving the Hfunction of two variables. These formulas are then used to obtain double summation formulas for the Hfunction of two variables. Our results are quite general in character and a number
Soft Gluons in Logarithmic Summations
, 1999
"... We demonstrate that all the known single and doublelogarithm summations for a parton distribution function can be unified in the CollinsSoper resummation technique by applying soft approximations appropriate in different kinematic regions to real gluon emissions. Neglecting the gluon longitudinal ..."
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We demonstrate that all the known single and doublelogarithm summations for a parton distribution function can be unified in the CollinsSoper resummation technique by applying soft approximations appropriate in different kinematic regions to real gluon emissions. Neglecting the gluon
Accurate floatingpoint summation
, 2005
"... Given a vector of floatingpoint numbers with exact sum s, we present an algorithm for calculating a faithful rounding of s into the set of floatingpoint numbers, i.e. one of the immediate floatingpoint neighbors of s. If the s is a floatingpoint number, we prove that this is the result of our a ..."
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Cited by 12 (1 self)
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to mantissa or exponent, they contain no branch in the inner loop, nor do they require extra precision: The only operations used are standard floatingpoint addition, subtraction and multiplication in one working precision, for example double precision. Moreover, in contrast to other approaches
ULTIMATELY FAST ACCURATE SUMMATION

, 2009
"... We present two new algorithms FastAccSum and FastPrecSum, one to compute a faithful rounding of the sum of floatingpoint numbers and the other for a result “as if” computed in Kfold precision. Faithful rounding means the computed result either is one of the immediate floatingpoint neighbors of th ..."
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Cited by 9 (0 self)
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. The algorithms require only standard floatingpoint addition, subtraction, and multiplication in one working precision, for example, double precision.
Accurate floating point summation
"... Abstract We present and analyze several simple algorithms for accurately summing n floating pointnumbers S = Pni=1 si, independent of how much cancellation occurs in the sum. Let f be thenumber of significant bits in the si. We assume a register is available with F> f significantbits. Then assumi ..."
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Cited by 1 (0 self)
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increase n slightly to b2Ff /(1 2f)c + 3 then all accuracycan be lost. This result extends work of Priest and others who considered double precision only (F> = 2f). We apply this result to the floating point formats in the (proposed revision ofthe) IEEE floating point standard. For example, a dot
Transformation and summation formulas for
, 1995
"... The double hypergeometric Kampé de Fériet series F 0:3 1:1 (1, 1) depends upon 9 complex parameters. We present three cases with 2 relations between those 9 parameters, and show that under these circumstances F 0:3 1:1 (1, 1) can be written as a 4F3(1) series. Some limiting cases of these transforma ..."
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The double hypergeometric Kampé de Fériet series F 0:3 1:1 (1, 1) depends upon 9 complex parameters. We present three cases with 2 relations between those 9 parameters, and show that under these circumstances F 0:3 1:1 (1, 1) can be written as a 4F3(1) series. Some limiting cases
Results 1  10
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182