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Handbook of mathematical formulas and integrals /
If there is a formula to solve a given problem in mathematics, you will find it in Alan Jeffrey's Handbook of Mathematical Formulas and Integrals. Thanks to its unique thumb-tab indexing feature, answers are easy to find based upon the type of problem they solve. The Handbook covers important f...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
San Diego :
Academic Press,
�1995.
|
| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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| 100 | 1 | |a Jeffrey, Alan. | |
| 245 | 1 | 0 | |a Handbook of mathematical formulas and integrals / |c by Alan Jeffrey. |
| 246 | 3 | 0 | |a Mathematical formulas and integrals |
| 260 | |a San Diego : |b Academic Press, |c �1995. | ||
| 300 | |a 1 online resource (xxiv, 410 pages) : |b illustrations | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 347 | |a text file | ||
| 347 | |b PDF | ||
| 504 | |a Includes bibliographical references (pages 397-399) and index. | ||
| 506 | |3 Use copy |f Restrictions unspecified |2 star |5 MiAaHDL | ||
| 533 | |a Electronic reproduction. |b [Place of publication not identified] : |c HathiTrust Digital Library, |d 2011. |5 MiAaHDL | ||
| 538 | |a Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002. |u http://purl.oclc.org/DLF/benchrepro0212 |5 MiAaHDL | ||
| 583 | 1 | |a digitized |c 2011 |h HathiTrust Digital Library |l committed to preserve |2 pda |5 MiAaHDL | |
| 588 | 0 | |a Print version record. | |
| 520 | |a If there is a formula to solve a given problem in mathematics, you will find it in Alan Jeffrey's Handbook of Mathematical Formulas and Integrals. Thanks to its unique thumb-tab indexing feature, answers are easy to find based upon the type of problem they solve. The Handbook covers important formulas, functions, relations, and methods from algebra, trigonometric and exponential functions, combinatorics, probability, matrix theory, calculus and vector calculus, both ordinary and partial differential equations, Fourier series, orthogonal polynomials, and Laplace transforms. Based on Gradshteyn and Ryzhik's Table of Integrals, Series, and Products, Fifth Edition (edited by Jeffrey), but far more accessible and written with particular attention to the needs of students and practicing scientists and engineers, this book is an essential resource. Affordable and authoritative, it is the first place to look for help and a rewarding place to browse. | ||
| 505 | 0 | 0 | |g 0 |t Quick Reference List of Frequently Used Data -- |g 0.1 |t Useful Identities |g 1 -- |g 0.2 |t Complex Relationships |g 2 -- |g 0.3 |t Constants |g 2 -- |g 0.4 |t Derivatives of Elementary Functions |g 3 -- |g 0.5 |t Rules of Differentiation and Integration |g 3 -- |g 0.6 |t Standard Integrals |g 4 -- |g 0.7 |t Standard Series |g 11 -- |g 0.8 |t Geometry |g 13 -- |g 1 |t Numerical, Algebraic, and Analytical Results for Series and Calculus -- |g 1.1 |t Algebraic Results Involving Real and Complex Numbers |g 25 -- |g 1.2 |t Finite Sums |g 29 -- |g 1.3 |t Bernoulli and Euler Numbers and Polynomials |g 37 -- |g 1.4 |t Determinants |g 47 -- |g 1.5 |t Matrices |g 55 -- |g 1.6 |t Permutations and Combinations |g 62 -- |g 1.7 |t Partial Fraction Decomposition |g 63 -- |g 1.8 |t Convergence of Series |g 66 -- |g 1.9 |t Infinite Products |g 71 -- |g 1.10 |t Functional Series |g 73 -- |g 1.11 |t Power Series |g 74 -- |g 1.12 |t Taylor Series |g 79 -- |g 1.13 |t Fourier Series |g 81 -- |g 1.14 |t Asymptotic Expansions |g 85 -- |g 1.15 |t Basic Results from the Calculus |g 86 -- |g 2 |t Functions and Identities -- |g 2.1 |t Complex Numbers and Trigonometric and Hyperbolic Functions |g 101 -- |g 2.2 |t Logarithms and Exponentials |g 112 -- |g 2.3 |t The Exponential Function |g 114 -- |g 2.4 |t Trigonometric Identities |g 115 -- |g 2.5 |t Hyperbolic Identities |g 121 -- |g 2.6 |t The Logarithm |g 126 -- |g 2.7 |t Inverse Trigonometric and Hyperbolic Functions |g 128 -- |g 2.8 |t Series Representations of Trigonometric and Hyperbolic Functions |g 133 -- |g 2.9 |t Useful Limiting Values and Inequalities Involving Elementary Functions |g 136 -- |g 3 |t Derivatives of Elementary Functions -- |g 3.1 |t Derivatives of Algebraic, Logarithmic, and Exponential Functions |g 139 -- |g 3.2 |t Derivatives of Trigonometric Functions |g 140 -- |g 3.3 |t Derivatives of Inverse Trigonometric Functions |g 140 -- |g 3.4 |t Derivatives of Hyperbolic Functions |g 141 -- |g 3.5 |t Derivatives of Inverse Hyperbolic Functions |g 142 -- |g 4 |t Indefinite Integrals of Algebraic Functions -- |g 4.1 |t Algebraic and Transcendental Functions |g 145 -- |g 4.2 |t Indefinite Integrals of Rational Functions |g 146 -- |g 4.3 |t Nonrational Algebraic Functions |g 158 -- |g 5 |t Indefinite Integrals of Exponential Functions -- |g 5.1 |t Basic Results |g 167 -- |g 6 |t Indefinite Integrals of Logarithmic Functions -- |g 6.1 |t Combinations of Logarithms and Polynomials |g 173 -- |g 7 |t Indefinite Integrals of Hyperbolic Functions -- |g 7.1 |t Basic Results |g 179 -- |g 7.2 |t Integrands Involving Powers of sinh(bx) or cosh(bx) |g 180 -- |g 7.3 |t Integrands Involving (a [plus or minus] bx)[superscript m] sinh(cx) or (a + bx)[superscript m] cosh(cx) |g 181 -- |g 7.4 |t Integrands Involving x[superscript m] sinh[superscript n] x or x[superscript m] cosh[superscript n] x |g 183 -- |g 7.5 |t Integrands Involving x[superscript m] sinh[superscript -n] x or x[superscript m] cosh[superscript -n] x |g 183 -- |g 7.6 |t Integrands Involving (1 [plus or minus] cosh x)[superscript -m] |g 185 -- |g 7.7 |t Integrands Involving sinh(ax)cosh[superscript -n] x or cosh(ax)sinh[superscript -n] x |g 185 -- |g 7.8 |t Integrands Involving sinh(ax + b) and cosh(cx + d) |g 186 -- |g 7.9 |t Integrands Involving tanh kx and coth kx |g 188 -- |g 7.10 |t Integrands Involving (a + bx)[superscript m] sinh kx or (a + bx)[superscript m] cosh kx |g 189 -- |g 8 |t Indefinite Integrals Involving Inverse Hyperbolic Functions -- |g 8.1 |t Basic Results |g 191 -- |g 8.2 |t Integrands Involving x[superscript -n] arcsinh(x/a) or x[superscript -n] arccosh(x/a) |g 193 -- |g 8.3 |t Integrands Involving x[superscript n] arctanh(x/a) or x[superscript n] arccoth(x/a) |g 194 -- |g 8.4 |t Integrands Involving x[superscript -n] arctanh(x/a) or x[superscript -n] arccoth(x/a) |g 195 -- |g 9 |t Indefinite Integrals of Trigonometric Functions -- |g 9.1 |t Basic Results |g 197 -- |g 9.2 |t Integrands Involving Powers of x and Powers of sin x or cos x |g 197 -- |g 9.3 |t Integrands Involving tan x and/or cot x |g 205 -- |g 9.4 |t Integrands Involving sin x and cos x |g 207 -- |g 9.5 |t Integrands Involving Sines and Cosines with Linear Arguments and Powers of x |g 211 -- |g 10 |t Indefinite Integrals of Inverse Trigonometric Functions -- |g 10.1 |t Integrands Involving Powers of x and Powers of Inverse Trigonometric Functions |g 215 -- |g 11 |t The Gamma, Beta, Pi, and Psi Functions -- |g 11.1 |t The Euler Integral and Limit and Infinite Product Representations for [Gamma] (x) |g 221 -- |g 12 |t Elliptic Integrals and Functions -- |g 12.1 |t Elliptic Integrals |g 229 -- |g 12.2 |t Jacobian Elliptic Functions |g 235 -- |g 12.3 |t Derivatives and Integrals |g 237 -- |g 12.4 |t Inverse Jacobian Elliptic Functions |g 237 -- |g 13 |t Probability Integrals and the Error Function -- |g 13.1 |t Normal Distribution |g 239 -- |g 13.2 |t The Error Function |g 242 -- |g 14 |t Fresnel Integrals, Sine and Cosine Integrals -- |g 14.1 |t Definitions, Series Representations, and Values at Intinity |g 245 -- |g 14.2 |t Definitions, Series Representations, and Values at Infinity |g 247 -- |g 15 |t Definite Integrals -- |g 15.1 |t Integrands Involving Powers of x |g 249 -- |g 15.2 |t Integrands Involving Trigonometric Functions |g 251 -- |g 15.3 |t Integrands Involving the Exponential Function |g 254 -- |g 15.4 |t Integrands Involving the Hyperbolic Function |g 256 -- |g 15.5 |t Integrands Involving the Logarithmic Function |g 256 -- |g 16 |t Different Forms of Fourier Series -- |g 16.1 |t Fourier Series for f(x) on -[pi] [less than or equal] x [less than or equal] [pi] |g 257 -- |g 16.2 |t Fourier Series for f(x) on -L [less than or equal] x [less than or equal] L |g 258 -- |g 16.3 |t Fourier Series for f(x) on a [less than or equal] x [less than or equal] b |g 258 -- |g 16.4 |t Half-Range Fourier Cosine Series for f(x) on 0 [less than or equal] x [less than or equal] [pi] |g 259 -- |g 16.5 |t Half-Range Fourier Cosine Series for f(x) on 0 [less than or equal] x [less than or equal] L |g 259 -- |g 16.6 |t Half-Range Fourier Sine Series for f(x) on 0 [less than or equal] x [less than or equal] [pi] |g 260 -- |g 16.7 |t Half-Range Fourier Sine Series for f(x) on 0 [less than or equal] x [less than or equal] L |g 260 -- |g 16.8 |t Complex (Exponential) Fourier Series for f(x) on -[pi] [less than or equal] x [less than or equal] [pi] |g 260 -- |g 16.9 |t Complex (Exponential) Fourier Series for f(x) on -L [less than or equal] x [less than or equal] L |g 261 -- |g 16.10 |t Representative Examples of Fourier Series |g 261 -- |g 16.11 |t Fourier Series and Discontinuous Functions |g 265 -- |g 17 |t Bessel Functions -- |g 17.1 |t Bessel's Differential Equation |g 269 -- |g 17.2 |t Series Expansions for J[subscript v](x) and Y[subscript v](x) |g 270 -- |g 17.3 |t Bessel Functions of Fractional Order |g 272 -- |g 17.4 |t Asymptotic Representations for Bessel Functions |g 273 -- |g 17.5 |t Zeros of Bessel Functions |g 273 -- |g 17.6 |t Bessel's Modified Equation |g 274 -- |g 17.7 |t Series Expansions for I[subscript v](x) and K[subscript v](x) |g 276 -- |g 17.8 |t Modified Bessel Functions of Fractional Order |g 277 -- |g 17.9 |t Asymptotic Representations of Modified Bessel Functions |g 278 -- |g 17.10 |t Relationships between Bessel Functions |g 278 -- |g 17.11 |t Integral Representations of J[subscript n](x), I[subscript n](x), and K[subscript n](x) |g 281 -- |g 17.12 |t Indefinite Integrals of Bessel Functions |g 281 -- |g 17.13 |t Definite Integrals Involving Bessel Functions |g 282 -- |g 17.14 |t Spherical Bessel Functions |g 283 -- |g 18 |t Orthogonal Polynomials -- |g 18.2 |t Legendre Polynomials P[subscript n](x) |g 286 -- |g 18.3 |t Chebyshev Polynomials T[subscript n](x) and U[subscript n](x) |g 290 -- |g 18.4 |t Laguerre Polynomials L[subscript n](x) |g 294 -- |g 18.5 |t Hermite Polynomials H[subscript n](x) |g 296 -- |g 19 |t Laplace Transformation -- |g 20 |t Fourier Transforms -- |g 21 |t Numerical Integration -- |g 21.1 |t Classical Methods |g 315 -- |g 22 |t Solutions of Standard Ordinary Differential Equations -- |g 22.2 |t Separation of Variables |g 323 -- |g 22.3 |t Linear First-Order Equations |g 323 -- |g 22.4 |t Bernoulli's Equation |g 324 -- |g 22.5 |t Exact Equations |g 325 -- |g 22.6 |t Homogeneous Equations |g 325 -- |g 22.7 |t Linear Differential Equations |g 326 -- |g 22.8 |t Constant Coefficient Linear Differential Equations -- Homogeneous Case |g 327 -- |g 22.9 |t Linear Homogeneous Second-Order Equation |g 330 -- |g 22.10 |t Constant Coefficient Linear Differential Equations -- Inhomogeneous Case |g 331 -- |g 22.11 |t Linear Inhomogeneous Second-Order Equation |g 333 -- |g 22.12 |t Determination of Particular Integrals by the Method of Undetermined Coefficients |g 334 -- |g 22.13 |t The Cauchy-Euler Equation |g 336 -- |g 22.14 |t Legendre's Equation |g 337 -- |g 22.15 |t Bessel's Equations |g 337 -- |g 22.16 |t Power Series and Frobenius Methods |g 339 -- |g 22.17 |t The Hypergeometric Equation |g 344 -- |g 22.18 |t Numerical Methods |g 345 -- |g 23 |t Vector Analysis -- |g 23.1 |t Scalars and Vectors |g 353 -- |g 23.2 |t Scalar Products |g 358 -- |g 23.3 |t Vector Products |g 359 -- |g 23.4 |t Triple Products |g 360 -- |g 23.5 |t Products of Four Vectors |g 361 |
| 505 | 0 | 0 | |t -- |g 23.6 |t Derivatives of Vector Functions of a Scalar t |g 361 -- |g 23.7 |t Derivatives of Vector Functions of Several Scalar Variables |g 362 -- |g 23.8 |t Integrals of Vector Functions of a Scalar Variable t |g 363 -- |g 23.9 |t Line Integrals |g 364 -- |g 23.10 |t Vector Integral Theorems |g 366 -- |g 23.11 |t A Vector Rate of Change Theorem |g 368 -- |g 23.12 |t Useful Vector Identities and Results |g 368 -- |g 24 |t Systems of Orthogonal Coordinates -- |g 24.1 |t Curvilinear Coordinates |g 369 -- |g 24.2 |t Vector Operators in Orthogonal Coordinates |g 371 -- |g 24.3 |t Systems of Orthogonal Coordinates |g 371 -- |g 25 |t Partial Differential Equations and Special Functions -- |g 25.1 |t Fundamental Ideas |g 381 -- |g 25.2 |t Method of Separation of Variables |g 385 -- |g 25.3 |t The Sturm-Liouville Problem and Special Functions |g 387 -- |g 25.4 |t A First-Order System and the Wave Equation |g 390 -- |g 25.5 |t Conservation Equations (Laws) |g 391 -- |g 25.6 |t The Method of Characteristics |g 392 -- |g 25.7 |t Discontinuous Solutions (Shocks) |g 396 -- |g 25.8 |t Similarity Solutions |g 398 -- |g 25.9 |t Burgers's Equation, the KdV Equation, and the KdVB Equation |g 400 -- |g 26 |t The z-Transform -- |g 26.1 |t The z-Transform and Transform Pairs |g 403 -- |g 27 |t Numerical Approximation -- |g 27.2 |t Economization of Series |g 411 -- |g 27.3 |t Pade Approximation |g 413 -- |g 27.4 |t Finite Difference Approximations to Ordinary and Partial Derivatives |g 415. |
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| 776 | 0 | 8 | |i Print version: |a Jeffrey, Alan. |t Handbook of mathematical formulas and integrals. |d San Diego : Academic Press, �1995 |w (DLC) 95002344 |w (OCoLC)31969977 |
| 856 | 4 | 0 | |u https://sciencedirect.uam.elogim.com/science/book/9780123825803 |z Texto completo |