CRC Concise Encyclopedia of MathematicsUpon publication, the first edition of the CRC Concise Encyclopedia of Mathematics received overwhelming accolades for its unparalleled scope, readability, and utility. It soon took its place among the top selling books in the history of Chapman & Hall/CRC, and its popularity continues unabated. Yet also unabated has been the d |
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Page 14
... BINOMIAL IDENTITY is ( x + y ) ( x + y − an ) ” — 1 n k n - k - 1 y ' ( x — ak ) ' — ' [ y — a ( n − k ) ] ” — * ( 4 ) k = 0 where ( ) is a BINOMIAL COEFFICIENT , a formula originally due to Abel ( Riordan 1979 , p . 18 ; Roman 1984 ...
... BINOMIAL IDENTITY is ( x + y ) ( x + y − an ) ” — 1 n k n - k - 1 y ' ( x — ak ) ' — ' [ y — a ( n − k ) ] ” — * ( 4 ) k = 0 where ( ) is a BINOMIAL COEFFICIENT , a formula originally due to Abel ( Riordan 1979 , p . 18 ; Roman 1984 ...
Page 15
... BINOMIAL IDENTITIES . See also BINOMIAL IDENTITY , Q- ABEL'S THEOREM References Abel, N. H. "Beweis eines Ausdrucks, von welchem die Binomial-Formel ein einzelner Fall ist." J. reine angew. Math. 1, 159Á60, 1826. Reprinted in Euvres ...
... BINOMIAL IDENTITIES . See also BINOMIAL IDENTITY , Q- ABEL'S THEOREM References Abel, N. H. "Beweis eines Ausdrucks, von welchem die Binomial-Formel ein einzelner Fall ist." J. reine angew. Math. 1, 159Á60, 1826. Reprinted in Euvres ...
Page 18
... BINOMIAL THEOREM , ABEL'S CONVERGENCE THEOREM , ABEL'S CURVE THEOREM , ABEL'S IMPOSSI- BILITY THEOREM , ABEL'S IRREDUCIBILITY THEOREM , ABELIAN THEOREM , Q - ABEL'S THEOREM Abel's Uniform Convergence Test Let { u , ( x ) } be a SEQUENCE ...
... BINOMIAL THEOREM , ABEL'S CONVERGENCE THEOREM , ABEL'S CURVE THEOREM , ABEL'S IMPOSSI- BILITY THEOREM , ABEL'S IRREDUCIBILITY THEOREM , ABELIAN THEOREM , Q - ABEL'S THEOREM Abel's Uniform Convergence Test Let { u , ( x ) } be a SEQUENCE ...
Page 28
... BINOMIAL COEFFICIENT and ( x ) „ is a FALLING FACTORIAL . The actuarial polynomials also satisfy the identity ∞ a ( −x ) = e -x k = 0 ( k + B ) n k ! Xck ( 8 ) ( Roman 1984 , p . 125 ; Whittaker and Watson 1990 , p . 336 ) . The first ...
... BINOMIAL COEFFICIENT and ( x ) „ is a FALLING FACTORIAL . The actuarial polynomials also satisfy the identity ∞ a ( −x ) = e -x k = 0 ( k + B ) n k ! Xck ( 8 ) ( Roman 1984 , p . 125 ; Whittaker and Watson 1990 , p . 336 ) . The first ...
Page 83
... BINOMIAL COEFFICIENT and [ n ] is the FLOOR FUNCTION . See also BOOLEAN FUNCTION , CHAIN , DILWORTH'S LEMMA , PARTIALLY ORDERED SET , WIDTH ( PARTIAL ORDER ) References Agnew , R. P. " Minimax Functions , Configuration Functions , and ...
... BINOMIAL COEFFICIENT and [ n ] is the FLOOR FUNCTION . See also BOOLEAN FUNCTION , CHAIN , DILWORTH'S LEMMA , PARTIALLY ORDERED SET , WIDTH ( PARTIAL ORDER ) References Agnew , R. P. " Minimax Functions , Configuration Functions , and ...
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Abramowitz Academic Press Addison-Wesley Algebraic ALGORITHM Amer ANGLE ARCHIMEDEAN SOLID Arfken AXIOM Bernoulli BESSEL FUNCTION BETA FUNCTION BINOMIAL COEFFICIENT Boca Raton BROCARD Calculus called Cambridge University Press CIRCLE Combinatorics COMPLEX NUMBER Comput CONIC Conjecture constant Continued Fractions Convex COORDINATES Coxeter CRC Press CUBE Cubic curve CYCLOID defined denoted Dictionary of Curious Differential Equations Differential Geometry digits Diophantine Equation Dirichlet Discrete Mathematics DISTRIBUTION DIVISOR DIVISOR FUNCTION Dover Encyclopedia of Integer England ffiffiffi finite FORMULA Geometry given Graph Theory GROUP HYPERGEOMETRIC identity Integer Sequences intersection JOHNSON SOLID KNOT Math Mathematica Mathematical Tables MATRIX N. J. A. Sequences Number Theory On-Line Version Penguin Dictionary PLANE points POLYGON POLYHEDRON POLYNOMIAL POLYOMINO PRIME Problem References RIEMANN ZETA FUNCTION SERIES Skiena Sloane Sloane's solution SPACE Springer-Verlag SQUARE Stegun SURFACE TANGENT THEOREM TION Topology TRANSFORM TRIANGLE VECTOR Weisstein Wiley York