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Luke Y.L. — Mathematical Functions and Their Approximations

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Íàçâàíèå: Mathematical Functions and Their Approximations

Àâòîð: Luke Y.L.

ßçûê:

Ðóáðèêà: Ìàòåìàòèêà/

Ñòàòóñ ïðåäìåòíîãî óêàçàòåëÿ: Ãîòîâ óêàçàòåëü ñ íîìåðàìè ñòðàíèö

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Ãîä èçäàíèÿ: 1975

Êîëè÷åñòâî ñòðàíèö: 585

Äîáàâëåíà â êàòàëîã: 02.07.2008

Îïåðàöèè: Ïîëîæèòü íà ïîëêó | Ñêîïèðîâàòü ññûëêó äëÿ ôîðóìà | Ñêîïèðîâàòü ID
Ïðåäìåòíûé óêàçàòåëü
 — Method      491 495 499 Airy functions      312 313 403 406 Approximation Expansion) Anger — Weber functions      413 426 Approximation of functions based on orthogonality properties of Chebyshev polynomials with respect to summation      469 475 Approximation of functions based on orthogonality properties of rational and polynomial      413 427 490 505 Approximation, , BCP      75 Approximation, Bessel functions, , RFP      364 365 Approximation, Bessel functions, , BCRF      411 412 Approximation, Bessel functions,       411 Approximation, Bessel functions, , TR      397 399 Approximation, Bessel functions, , , BCP      411 412 Approximation, Bessel functions, , BCP      411 412 Approximation, Bessel functions, , BCP and BCRF      411 412 Approximation, Bessel functions, , repeated integrals of      411 Approximation, Bessel functions,       412 Approximation, Bessel functions, R      380 395 Approximation, Bessel functions, RF      361 366 379 Approximation, Bessel functions, RFP      412 Approximation, best in sense of -method      491 493—495 Approximation, best in sense of Chebyshev      490 493 Approximation, best in sense of least square      491 Approximation, best in sense of mean square      493 Approximation, best in sense of Pade      493—495 Approximation, binomial function,       27—31 Approximation, binomial function, , BCP and BCRF      75 Approximation, binomial function, , BCP      76 Approximation, binomial function, , , RF      28 Approximation, binomial function, , BCP      76 Approximation, binomial function, Newton-Raphson process      29 Approximation, binomial function, RFP      28 30 75 Approximation, Debye functions, RFP      76 Approximation, economized      496 Approximation, error functions, Erf(z), Erfi(z), BCRF      152 Approximation, error functions, Erfc(z), BCRF      151 152 Approximation, error functions, inverse      152 Approximation, error functions, P      512 Approximation, error functions, repeated integrals, R      101 102 Approximation, error functions, RFP      124 128 Approximation, error functions, TR      134 137 Approximation, exponential function, , RFP      31 33 Approximation, exponential function, , BCP and BCRF      75 76 Approximation, exponential function, exp(), as a sum of exponentials      76 Approximation, exponential function, RF      76 Approximation, exponential function, RFP      46 51 386 Approximation, exponential integral, BCRF      150 Approximation, exponential integral, RF      106 110 150 Approximation, exponential integral, RFP      88 93 107 110 114 150 Approximation, Fresnel integrals, BCRF      153 Approximation, Fresnel integrals, P      152 153 Approximation, Fresnel integrals, RF      139 Approximation, functions, defined by a differential equation, P and RF      554 Approximation, gamma function, , BCRF      23 Approximation, gamma function, , BCRF      22 Approximation, gamma function, , BCP      22 33 Approximation, gamma function, , RF      7 23 Approximation, gamma function, , RFP      7 100 Approximation, gamma function, logarithmic derivative, BCP, BCRF, RFP      23 Approximation, gamma function, RF      13 16 Associated Bessel function      413 427 Asymptotic expansions, large variable      315 Asymptotic expansions, references to      154 (see also modifiers such as Bessel functions) Basic series      446 Ber, bei functions      312 404 Approximation Bernoulli and generalized Bernoulli polynomials      505 507 Bernoulli numbers      506 Bessel functions, Airy functions, connection with      312 313 Bessel functions, approximation, see Approximation associated      413 427 Bessel functions, asymptotic expansions, large variable      315 Bessel functions, ber, bei functions, connection with      312 Bessel functions, bibliographic and numerical data      403 412 Bessel functions, computation of, by use of recurrence formulas      380 395 509 Bessel functions, computation of, by use of trapezoidal type integration formulas      395 399 Bessel functions, confluent hypergeometric function, connection with      294 311 Bessel functions, definitions, connecting relations, power series      311 313 Bessel functions, derivatives with respect to the order      360 405 Bessel functions, difference-differential properties      313 314 Bessel functions, expansion, expansions in series of      (see Expansion) Bessel functions, G-function, connection with      302 307 309 Bessel functions, incomplete      414 417 426 Bessel functions, inequalities      366 396 399 403 Bessel functions, integral representations      396 398 Bessel functions, integrals involving      187 315 316 403 405 408 411 412 414 426 509 510 Bessel functions, ker, kei functions, connection with      312 Bessel functions, large order      393 398 Bessel functions, multiplications theorems      185 360 Bessel functions, products of      219 304 310 314 Bessel functions, ratio , inequalities for      366 400 Bessel functions, repeated integrals of       397 398 Bessel functions, series of      403 405 406 Bessel functions, tables, description of and references to      404 411 Bessel functions, Wronskians      314 Bessel functions, zeros and extrema of      365 403 406 407 412 Bessel polynomials      229 433 Bessel's inequality      430 Best approximation      (see Approximation) Beta function, complete      298 Beta function, incomplete      297 299 Beta transform      160 Binomial coefficient      11 12 Binomial function      24 35 Expansion Inequalities) Catalan' constant      511 515 Chebyshev polynomials of the first kind      (see also Jacobi polynomials) Chebyshev polynomials of the first kind, approximations in series of      490 493 Chebyshev polynomials of the first kind, approximations in series of (based on orthogonality properties with respect to summation)      469 473 491 Chebyshev polynomials of the first kind, coefficients for expansion of integrals of functions in series of      464 469 Chebyshev polynomials of the first kind, connection with Pade approximation for square root      29 Chebyshev polynomials of the first kind, definition and basic properties      434 436 453 463 Chebyshev polynomials of the first kind, evaluation of series of by use of backward recurrence formula      478 481 482 Chebyshev polynomials of the first kind, expansion of in series of      454 455 459 461 Chebyshev polynomials of the first kind, expansions in series of (based on orthogonality property with respect to integration)      (see also Expansion) Chebyshev polynomials of the first kind, expansions in series of (based on orthogonality property with respect to integration), asymptotic estimate of coefficients      448 452 Chebyshev polynomials of the first kind, expansions in series of (based on orthogonality property with respect to integration)evaluation of coefficients      443 448 Chebyshev polynomials of the first kind, expressed in powers of x      453 458 459 462 463 Chebyshev polynomials of the first kind, integrals involving      455 456 459 460 464 469 Chebyshev polynomials of the first kind, Jacobi polynomial, connection with      434 453 Chebyshev polynomials of the first kind, minimax, least and mean square properties      490 493 Chebyshev polynomials of the first kind, orthogonality property with respect to integration      434 436 455 459 Chebyshev polynomials of the first kind, powers of x, expressed in terms of      454 457 459 461 Chebyshev polynomials of the first kind, solution of differential and integral equations by expansion in series of      464 469 500 504 Chebyshev polynomials of the first kind, summation      432 469 473 Chebyshev polynomials of the second kind      (see also Jacobi polynomials) Chebyshev polynomials of the second kind, approximations in series of (based on orthogonality properties with respect to summation)      473 475 Chebyshev polynomials of the second kind, connection with Pade approximation for square root      29 Chebyshev polynomials of the second kind, definition and basic properties      434 436 453 463 Chebyshev polynomials of the second kind, integrals involving      455 456 Chebyshev polynomials of the second kind, Jacobi polynomial, connection with      434 453 Chebyshev polynomials of the second kind, orthogonality property with respect to integration      434 436 455 Chebyshev polynomials of the second kind, summation      432 473 475 Chebyshev, best approximation in sense of      490 493 Christoffel — Darboux formulas      432 433 Circular functions      (see Sine and cosine and Tangent) Clebsch — Gordan coefficients      168 Collocation      498 Computation and check of the tables      509 512 Computation of series of functions where functions satisfy a linear finite difference equation      475 482 Computation, by use of recurrence formulas      98 100 102 219 220 320 380 395 464 468 475 482 483 489 509—512 Confluence principle and theorems      179 183 Constants, mathematical table of      514 515 Continued fractions      (see Approximation (RFP)) Converging factors      145 148 404 Cosine      (see Sine and cosine) Cosine integral      (see Sine and cosine integrals) Cotangent      (see Tangent) Coulomb wave functions      297 300 Cylinder function      311 D operator      507 509 Debye functions      76 Delta operator      507 509 Difference equations      (see Recurrence formulas) Differential, integral and functional equations      (see Approximation Expansion) Dilogarithm      67 511 Dixon's equation      164 Dominance in asymptotic expansions      201 Dominance in solutions of difference equations      483 E-function      176 Economized approximation      496 Elliptic functions and integrals      279 299 511 Error functions      88 94 102 119 138 145 148 509 510 Expansion) Euler transforms      189 190 Euler — Mascheroni constant, y      1 512 515 Expansion, Airy functions      312 313 Expansion, Bessel functions, , BF      317 Expansion, Bessel functions,       317 319 500 504 Expansions      (see The discussion below) Exponential function      31 33 42 52 74 76 509 514 Exponential integral      88 93 96 99 103 114 143 145 509 510 Fourier coefficients      430 442 Fourier series, convergence of      443 Fourier transform, of G-function      189 Fresnel integrals      139 142 148 219 303 Expansion) G-function      154 256 G-function, analytic continuation      178 179 G-function, approximation of      (see Approximation) G-function, asymptotic expansion, large parameter      216 218 G-function, definition      170 171 G-function, differential equation and solutions      192 193 G-function, elementary properties      176 178 G-function, expansions      (see Expansion) G-function, expressed as a named function      306 310 G-function, hypergeometric functions and named functions, connection with      300 310 G-function, inequalities      255 256 G-function, integral representations      162 170 187 190 G-function, integrals involving      186 189 G-function, large variable      199 206 G-function, multiplication theorems      184 185 G-function, named functions expressed in terms of      300 306 G-function, references to      154 Gamma function      1 23 Gamma function, approximation      (see Approximation) Gamma function, asymptotic expansion      7 10 11 12 Gamma function, definite integrals expressed in terms of      161 163 186 Gamma function, expansion      (see Expansion) Gamma function, inequalities      17 20 Gamma function, logarithmic derivative of      (see Psi-function) Gamma function, numerical values for certain fractional arguments      515 Gamma function, power series and other expansions      1 7 Gamma function, references      20 Gamma function, tables, references to      21 22 74 147 Gegenbauer polynomial      434 436 h-transform      187 Hankel functions      305 306 309 312 315 316 319 367 Hankel transforms      187 444 Hermite polynomials      434 436 Hyperbolic functions      (see Sine and cosine and tangent and cotangent) Hypergeometric function (confluent), , U-function, approximation of      (see Approximation) Hypergeometric function (confluent), , U-function, asymptotic expansion, large parameter(s)      182 183 292 293 Hypergeometric function (confluent), , U-function, bibliographic and numerical data      296 297 Hypergeometric function (confluent), , U-function, confluence      180 284 Hypergeometric function (confluent), , U-function, contiguous relations      285 286 Hypergeometric function (confluent), , U-function, difference-differential properties      285 286 Hypergeometric function (confluent), , U-function, differential equations and solutions      287 290 Hypergeometric function (confluent), , U-function, expansions in series of Jacobi polynomials, Chebyshev polynomials, etc.      (see Expansion) Hypergeometric function (confluent), , U-function, G-function, connection with      301 307 Hypergeometric function (confluent), , U-function, inequalities      295 Hypergeometric function (confluent), , U-function, integral representations      284 Hypergeometric function (confluent), , U-function, integrals of      296 Hypergeometric function (confluent), , U-function, Kummer relations      288 Hypergeometric function (confluent), , U-function, large variable      291 292 Hypergeometric function (confluent), , U-function, products of      286 287 303 308 310 Hypergeometric function (confluent), , U-function, references      296 Hypergeometric function (confluent), , U-function, tables, description of and references to      296 297 Hypergeometric function (confluent), , U-function, uniform      85 89 Hypergeometric function (confluent), , U-function, Whittaker functions      284 297 Hypergeometric Hypergeometric Incomplete Hypergeometric function (confluent), , U-function, Wronskians      291 Hypergeometric function (confluent), , U-function, zeros      90 296 Hypergeometric function (Gaussian),       257 283 Hypergeometric function (Gaussian), , analytic continuation      263 265 Hypergeometric function (Gaussian), , approximation of      (see Approximation) Hypergeometric function (Gaussian), , bibliographic and numerical data      279 283 Hypergeometric function (Gaussian), , confluence principle      180 Hypergeometric function (Gaussian), , contiguous relations      258 259 Hypergeometric function (Gaussian), , difference-differential properties      257 259 Hypergeometric function (Gaussian), , differential equations and solutions      260 270 Hypergeometric function (Gaussian), , evaluation of, for special values of argument      271 273 Hypergeometric function (Gaussian), , expansions in series of Jacobi polynomials, Chebyshev polynomials, etc.      (see Expansion) Hypergeometric function (Gaussian), , inequalities      278 Hypergeometric function (Gaussian), , integral representations      259 260 Hypergeometric function (Gaussian), , Kummer relations      262 Hypergeometric function (Gaussian), , named functions, expressed in terms of      298 299 434 Hypergeometric function (Gaussian), , orthogonal polynomials, classical, connection with      434 Hypergeometric function (Gaussian), , quadratic transformations      270 271 Hypergeometric function (Gaussian), , references      279 Hypergeometric function (Gaussian), , tables, description of and references to      279 283 Hypergeometric function (Gaussian), , Wronskians      270 Hypergeometric function (generalized),       154 256 Hypergeometric function (generalized), , analytic continuation      179 Hypergeometric function (generalized), , approximation of      (see Approximation) Hypergeometric function (generalized), , asymptotic expansions, large parameter(s)      182 183 452 Hypergeometric function (generalized), , confluence principle and theorems      179 183 Hypergeometric function (generalized), , contiguous relations      159 Hypergeometric function (generalized), , convergence of series      155 Hypergeometric function (generalized), , differential equations and solutions      190 191 Hypergeometric function (generalized), , differential-difference properties      159 Hypergeometric function (generalized), , evaluation of for special values of argument and parameters      163 170 271 273 437 438 441 Hypergeometric function (generalized), , expansion theorem for large parameter      182 183 Hypergeometric function (generalized), , expansions in series of Jacobi polynomials, Chebyshev polynomials, etc.      (see Expansion) Hypergeometric function (generalized), , G-function, connection with      174 175 300 301 306 Hypergeometric function (generalized), , inequalities      155 252 256 Hypergeometric function (generalized), , integral representations and integrals involving      160 163 187 Hypergeometric function (generalized), , large variable      206 213 Hypergeometric function (generalized), , polynomial      156 Hypergeometric function (generalized), , products of      157 158 Hypergeometric function (generalized), , special functions, references to      154 Hypergeometric function (generalized), , zeros      257 Incomplete gamma function      77 153 Incomplete gamma function, bibliographic and numerical data      143 149 Incomplete gamma function, computation of      97 103 Incomplete gamma function, inequalities      95 97 Incomplete gamma function, tables, references to      143 149 Inequalities for Bessel functions      366 396 403 Inequalities for binomial functions      34 35 Inequalities for error functions      96 137 138 Inequalities for exponential function      51 52 Inequalities for exponential integral      96 97 Inequalities for G-functions, a certain class of      255 256 Inequalities for gamma functions      17 18 Inequalities for hyperbolic tangent      60 Inequalities for hypergeometric functions, a certain class of      252 255 278 279 295 Inequalities for incomplete gamma functions      96 97 Inequalities for logarithmic derivative of the gamma function      19 Inequalities for logarithmic functions      41 42 73 74 Inequalities for sinh, inverse of      73 Inequalities for tangent and its inverse      60 61 72 73 Inequalities Inverse tangent integral      67 511 Integral equations, solution of by expansion in series of Chebyshev polynomials of the first kind      (see Expansion) Integrals      (see appropriate modifiors such as Bessel functions integrals) Integration, numerical      (see Approximation integrals) Inverse circular and hyperbolic functions      61 (see also Approximation Expansion) Jacobi and associated Jacobi function      244 433 449 Jacobi polynomial, connection with      434 Jacobi polynomials, application of in approximation of functions by polynomials and rational functions      497 498 Jacobi polynomials, asymptotic expansion for large order      438 439 Jacobi polynomials, definition and basic properties      235 237 242 243 434 452 Jacobi polynomials, evaluation and estimation of coefficients for a given function when expanded in series of      443 452 Jacobi polynomials, expansion of functions in series of      442 443 446 448 Jacobi polynomials, extended and generalized      227 231 235 447 Jacobi polynomials, integrals involving      439 440 Jacobi polynomials, orthogonality property      434 436 K — Transform      187 Ker and kei functions (also known as Kelvin functions)      312 404 Approximation Expansion)
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