Электронная библиотека Попечительского советамеханико-математического факультета Московского государственного университета
 Главная    Ex Libris    Книги    Журналы    Статьи    Серии    Каталог    Wanted    Загрузка    ХудЛит    Справка    Поиск по индексам    Поиск    Форум Авторизация Поиск по указателям     Jordan C. — Calculus of Finite Differences Обсудите книгу на научном форуме Нашли опечатку?Выделите ее мышкой и нажмите Ctrl+Enter Название: Calculus of Finite Differences Автор: Jordan C. Аннотация: This book, a result of nineteen years’ lectures on the Calculus of Finite Differences, Probability, and Mathematical Statistics in the Budapest University of Technical and Economical Sciences, and based on the venerable works of Stirling, Euler and Boole, has been written especially for practical use, with the object of shortening and facilitating the labours of the Computer. With this aim in view, some of the old and neglected, though useful, methods have been utilized and further developed: as for instance Stirling’s methods of summation, Boole’s symbolical methods, and Laplace’s method of Generating Functions, which last is especially helpful for the resolution of equations of partial differences. Язык: Рубрика: Математика/Анализ/Учебники по элементарному анализу/ Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Издание: 2-nd edition Год издания: 1950 Количество страниц: 652 Добавлена в каталог: 09.04.2005 Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID Предметный указатель expansion into powers      146 202 204 numbers, table of      266 numbers, table of      152 , numbers, table of      172 functions      347 functions by a definite integral      351 functions into Boole series      438 functions into Euler polynomials      349 functions into Euler series      349 functions, derivatives of      352 functions, expansion by digamma function      351 functions, expansion into Boole polynomials      348 numbers, table of      449 450 numbers, table of      155 numbers, table of      154 numbers table of      429 Addition of differences, method of      76 Alternate functions      92—94 Alternate functions, sum of      320 324 Alternate functions, summation by parts      108 Alternate reciprocal powers am numbers, table of      232 251 Alternate reciprocal powers, expressed by sums      251 Alternate reciprocal powers, generating function of      251 Alternate reciprocal powers, sum of      251 Antilogarithmic tables      399 402 Approximation by Bernoulli's probability function      432 Approximation by incomplete B function      428 Approximation by incomplete r function      426 Approximation by Laplace's probability function      430 Approximation by Poisson's probability function      431 Approximation, principle of least squares      422 Approximation, principle of moments      422 Arithmetical progression      79 Bayes’ Theorem      86 Bernoulli numbers      23 62 130 140 181 182 227 229 Bernoulli numbers by Cmi      229 599 Bernoulli numbers by Stirling numbers      219 236 Bernoulli numbers, ex-pressed by b      250 Bernoulli numbers, symbolical formula of      233 Bernoulli numbers, table of      234 235 Bernoulli polynomials into Boole polynomials      323 Bernoulli polynomials into Euler polynomials      308 Bernoulli polynomials into Fourier series      242 Bernoulli polynomials, expansion into Bernoulli polynomials first kind      276 Bernoulli polynomials, expansion into factorials      235 Bernoulli polynomials, extrema      240 Bernoulli polynomials, first kind      60 62 181 230 Bernoulli polynomials, generating function of      279 Bernoulli polynomials, limits      272 Bernoulli polynomials, multiplication formula of      252 Bernoulli polynomials, roots      240 Bernoulli polynomials, second kind      64 72 134 147 224 265 277 Bernoulli polynomials, symmetry      268 Bernoulli series      253 Bernoulli series, second kind      280 Bernoulli’s solution of numerical equations      494 Beta functions      50 80 Binomial coefficients      62—70 Binomial coefficients, Cauchy’s formula of      73 Binomial coefficients, generalised      70 Binomial moments      424 Binomial moments by Stirling numbers      267 147 Binomial moments, computation of      460 613 Binomial moments, expressed by Bernoulli numbers      249 278 Binomial moments, generating function of      258 279 284 Boole polynomials      64 317 321 Boole polynomials, expanded into Bernoulli polynomials second kind      321 Boole series      323 Boole’s first summation formula      315 354 Boole’s first summation formula, second summation formula      323 Cauchy’s formula for binomials      24 41 48 68 Cauchy’s formula, integral      41 Cauchy’s formula, rule for summing binomials      73 133 135 136 Cauchy’s formula, rule of multiplication of series      25 Changing the origin of intervals      219 Changing the origin of intervals the length of intervals      220 Combinations, difference equation giving number of      578 Construction of tables      363 Correlation, coefficient of      455 cot z expansion of      259 Cotes numbers      224 388 Cotes numbers, determined by Stirling numbers      514 Decomposition into partial fractions      34—40 335 Derivatives expressed by operation      197 Derivatives expressed by differences      164—165 Difference equation linear variable coefficients first order      576 Difference equation, complete      583 Difference equation, homogeneous by Laplace’s method      579 Difference equation, reducible      584 Difference equation, resolution by Andre’s method      587 Difference equation, resolution by generating functions      586 Difference equations by method of arbitrary constants      569 Difference equations with complex roots      554 Difference equations with multiple roots      549—552 Difference equations with negative roots      552 Difference equations, characteristic equation with single roots      542 Difference equations, genesis of      543 Difference equations, linear mixed      632 Difference equations, linear, constant coefficients, complete      557—564 Difference equations, linear, constant coefficients, homogeneous      545 Difference equations, particular solution obtained directly      564 Difference equations, resolved by generating functions      572 Difference of a function with negative argument      5 69 Difference of a product      94—98 Differences (advancing)      2 Differences (advancing), central      15 Differences (advancing), divided      18 Differences (advancing), receding      14 Differences expressed by derivatives      189—192 Differences expressed by means      9 Differences expressed by the operation      200 Differences expressed by values of the function      8 Digamma function      58—60 Digamma function by Bernoulli series, of the second kind      283 Digamma function by powers series      327 Digamma function by reciprocal powers      328 Digamma function expressed by Bernoulli series      256 Digamma function, sum of      1 Displacement      6 Endpanel interpolation formula      379 Euler numbers      23 300 Euler numbers limits of      302 Euler polynomials      62 115 288 Euler polynomials, extrema of      293 Euler polynomials, generating function of      309 Euler polynomials, inverse difference of      297 Euler polynomials, inverse means of      297 Euler polynomials, limits of      302 Euler polynomials, multiplication theorem of      311 Euler polynomials, roots of      293 Euler polynomials, symmetry of      292 Euler’s constant      27 55 58 129 130 148 341 Euler’s formula for f functions      55 83 Euler’s formula for trigonometric functions      90 Euler’s polynomials expanded into Bernoulli polynomials      295 Expansion of a function by decomposition into, partial fractions      34 40 Expansion of a function of functions      31 33 204 205 Expansion of a function, complex intergrals      40—41 Expansion of a function, difference equations      41—44 Expansion of a function, symbolical methods      11 Expansion of functions into Bernoulli polynomials      307 248 250 Expansion of functions into Bernoulli series      253 Expansion of functions into binomials      74 Expansion of functions into Boole polynomials      322 Expansion of functions into Boole series      323 Expansion of functions into Euler polynomials      307 Expansion of functions into Euler series      313 Expansion of functions into Legendre polynomials      434 Expansion of functions into Newton series      74 358 Expansion of functions into orthogonal series      447 Expansion of functions into polynomials      355 Expansion of functions into powers      29—34 Expansion of functions into reciprocal factorials      192 212 Expansion of functions into reciprocal powers      212 Exponential functions      87—88 Faa Bruno’s expansion of a function of function      33 205 Factorial moments determined by generating functions      208 Factorials      45—53 Factorials, computation of      52 Factorials, definition by gamma functions      56 Factorials, difference of      51 Factorials, expansion into powers      142 Factorials, mean of      52 Fibonacci numbers      548 First panel interpolation formula      378 Fourier series      242 426 463 Fourier series, Newton series      289 Functions expressed by differences      10 Functions expressed by means      10 Functions expressed whose differences or means are zero      94 Functions expressed, product of two      94—98 G polynomials      426 473 Gamma function      53—56 Gamma function, computation of      55 Generating functions      20 29 109 Generating functions of binomial coefficients      71 73 Generating functions, determination by difference equations      27 Graduation by least squares and orthogonal polynomials      456 Gregory’s formula of numerical integration      525 Hermite polynomials      63 426 467 Hospital’s rule      133 Hyperbolic functions      38 Incomplete B function      83—37 Indefinite sum      101 Indefinite sum by difference equation      109 Indefinite sum by inversion      103 Indefinite sum by summation by parts      105 Infinite series, differences and means of      110 Interpolation by Bessel's formula      373 Interpolation formula, general case      420 421 Interpolation formula, precision of      417—420 Interpolation in a double entry table      532 Interpolation, case of three variables      541 Interpolation, Everett's formula      376 Interpolation, formula needing no differences      390 Interpolation, Gauss' formulae      363 Interpolation, Newton's formula      361 Interpolation, Stirling's formula      374 Inverse difference      101 Inverse difference, Everett      381 Inverse difference, Formula needing no differences      411 Inverse difference, Lagrange      390 Inverse mean      111—116 Inverse mean of a function      306 Inversion of sums and series      183 185 Iteration, method of, for solving numerical equations      492 Lacroix’s difference equation giving the sum of x      596 Lagrange’s formula      360 Lagrange’s formula, interpolation formula      386 Lagrange’s formula, polynomial      385 Legendre polynomials      389 434 Legendre polynomials, roots of the      435 Leibnitz’ formula of higher derivatives      96 143 167 log, Bernoulli series, second kind      284 287 log, expansion into Bernoulli polynomials, second kind      280 log, tables      399 402 407 409 410 Maclaurin series      201 216 246 Maclaurin — Euler summation formula      260 265 Mean of a function      7 Mean of a function of a product      98—99 Mean of a function, central      15 Mean, arithmetical      433 Mean, binomial moment      448 Mean, orthogonal moment      450 Mean-square deviation      427 433 452 Median      433 Midpanel interpolation formula      397 MODE      433 Moments, actorial      424 Moments, binomial      424 Moments, computation of binomial moments      615 Moments, expressed by semi-invariants      211 Moments, power      163 164 812 Newton — Rapbson solution of numerical equations      489 Newton's binomial formula      49 Newton's binomial formula, expansion      26 75 76 77 79 164 189 219 357 Newton's binomial formula, expansion for unequal intervals      20 Newton's binomial formula, formula for two variables      531 Numerical integration      512 Numerical integration, Euler — Maclaurin formula      525 Numerical resolution of difference equations      527 Orthogonal polynomials      436 Orthogonal polynomials, central value of the      445 Partial difference equations      604 Partial difference equations four independent variables      638 Partial difference equations, Boole's symbolical method      616 Partial difference equations, Fourier, Legendre, Ellis' method      619 Partial difference equations, Laplace's method of generating functions      607 Partial difference equations, linear, constant coefficients      60 Partial difference equations, three independent variables      633 Partial differences      530 Pascal’s arithmetical triangle      612 Power moments expressed by      6 Power moments expressed by operations      197 Power series, sum of      246 Powers expressed by factorials      181 Probability by Stirling numbers      166 177 Probability function, binomial moments of      424 Probability function, expanded into G polynomials      483 484 Probability function, table of      400 403 408 Probability, coincidences      595 610 Probability, determination of, by sums      140 Probability, Examples on, Bayes' theorem      86 Probability, parcours      630 633 638 Probability, problem of      575 Probability, problem of points      608 Probability, repeated trials      86 599 615 Probability, ruin      550 627 Product of prime numbers, decomposition of      179 181 Progression, arithmetical      118 Progression, geometrical      124 Rational fraction, sum of      335 Reciprocal factorial, derivation of      337 Reciprocal factorial, expanded into reciprocal powers      193—195 Reciprocal factorial, integration of      194 338 Reciprocal factorial, sum of      121 Reciprocal powers, alternate sum of      244 Reciprocal powers, difference of      194 Reciprocal powers, sum of      194 244 214 325 338 Reciprocal powers, sum of, by Stirling numbers      338 Regula Falsi      366 486 Remainder of the expansion into a series of polynomials      356 Remainder of the expansion, maximum of      362 Rule of false position      366 486 Schlomilch's expansion formula      31 204 Semi-invariants of Thiele      204 210 Semi-invariants of Thiele, expressed by moments      211 Simmons theorem      87 Simultaneous linear difference equation      601 Stirling numbers of the second lcind      32 134 168 179 Stirling numbers, formulae containing      182 185—189 Stirling polynomials      224—229 Sum without repetition transformed      153—158 Summation by parts      105 106 107 Summation by parts of alternate function      108 140 320 324 Symbolical calc.      7—14 tan z, expansion of      259 Tangent coefficients      130 298 Taylor’s series      13 165 189 Tchebichef polynomial      389
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