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Spiegel M.R. — Mathematical Handbook of Formulas and Tables
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Название: Mathematical Handbook of Formulas and TablesАвтор: Spiegel M.R. Аннотация: Book Description
Язык: Рубрика: Математика /Справочники /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 1968Количество страниц: 271Добавлена в каталог: 21.10.2004Операции: Положить на полку |
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Addition formulas for Bessel functions 145 Addition formulas for elliptic functions 180 Addition formulas for Hermite polynomials 152 Addition formulas for hyperbolic functions 27 Addition formulas for trigonometric functions 15 Agnesi, witch of 43 Algebraic equations, solutions of 32 33 Amplitude of complex number 22 Amplitude of elliptic integral 179 Angle between lines in a plane 35 Angle between lines in space 47 Annuity, amount of 201 242 Annuity, present value of 243 Anti-derivative 57 Antilogarithms, common 23 195 204 205 Antilogarithms, natural or Napierian 24 226 227 Archimedes, spiral of 45 Area integrals 122 Argand diagram 22 Arithmetic mean 185 Arithmetic series 107 Arithmetic-geometric series 107 Associated Laguerre polynomials 155 156 Associated Laguerre polynomials, generating function for 155 Associated Laguerre polynomials, orthogonal series for 156 Associated Laguerre polynomials, orthogonality of 156 Associated Laguerre polynomials, recurrence formulas for 156 Associated Laguerre polynomials, special 155 Associated Laguerre polynomials, special results involving 156 Associated Legendre functions 149 150 Associated Legendre functions of the first kind 149 Associated Legendre functions of the second kind 150 Associated Legendre functions, generating function for 149 Associated Legendre functions, orthogonal series for 150 Associated Legendre functions, orthogonality of 150 Associated Legendre functions, recurrence formulas for 149 Associated Legendre functions, special 149 Associative law 117 Asymptotes of hyperbola 39 Asymptotic expansions or formulas for Bernoulli numbers 115 Asymptotic expansions or formulas for Bessel functions 143 Asymptotic expansions or formulas for gamma function 102 Base of logarithms 23 Base of logarithms, change of 24 Base of logarithms, definition of 140 Base of logarithms, differential equation for 141 Base of logarithms, graphs of 141 Ber and Bei functions 140 141 Bernoulli numbers 98 107 114 115 Bernoulli numbers, asymptotic formula for 115 Bernoulli numbers, definition of 114 Bernoulli numbers, relationship to Euler numbers 115 Bernoulli numbers, series involving 115 Bernoulli numbers, table of first few 114 Bernoulli's differential equation 104 Bessel functions 136—145 Bessel functions of first kind of order n 136 137 Bessel functions of order half an odd integer 138 Bessel functions of second kind of order n 136 137 Bessel functions, addition formulas for 145 Bessel functions, asymptotic expansions of 143 Bessel functions, definite integrals involving 142 143 Bessel functions, generating functions for 137 139 Bessel functions, graphs of 141 Bessel functions, indefinite integrals involving 142 Bessel functions, infinite products for 188 Bessel functions, integral representations for 143 Bessel functions, orthogonal series for 144 145 Bessel functions, recurrence formulas for 137 Bessel functions, tables of 244—249 Bessel functions, zeros of 250 Bessel's differential equation 106 136 Bessel's differential equation, general solution of 106 137 Bessel's differential equation, transformed 106 Bessel's modified differential equation 138 Bessel's modified differential equation, general solution of 139 beta function 103 Beta function, relationship of to gamma function 103 Biharmonic operator 120 Biharmonic operator in curvilinear coordinates 125 Binomial coefficients 3 Binomial coefficients, properties of 4 Binomial coefficients, table of values for 236 237 Binomial distribution 189 Binomial formula 2 Binomial series 2 110 Bipolar coordinates 128 129 Bipolar coordinates, Laplacian in 128 Branch, principal 17 Briggsian logarithms 23 Cardioid 41 42 44 Cassini, ovals of 44 Catalan's constant 181 Catenary 41 Cauchy or Euler differential equation 105 Cauchy — Schwarz inequality 185 Cauchy — Schwarz inequality for integrals 186 Cauchy's form of remainder in Taylor series 110 Chain rule for derivatives 53 Characteristic 194 Chebyshev polynomials 157—159 Chebyshev polynomials of first kind 157 Chebyshev polynomials of second kind 158 Chebyshev polynomials, generating functions for 157 158 Chebyshev polynomials, orthogonal series for 158 159 Chebyshev polynomials, orthogonality of 158 159 Chebyshev polynomials, recursion formulas for 158 159 Chebyshev polynomials, relationships involving 159 Chebyshev polynomials, special 157 158 Chebyshev polynomials, special values of 157 159 Chebyshev's differential equation 157 Chebyshev's differential equation, general solution of 159 Chebyshev's inequality 186 Chi square distribution 189 Chi square distribution, percentile values for 259 Circle, area of 6 Circle, equation of 37 Circle, involute of 43 Circle, perimeter of 6 Cissoid of Diocles 45 Common antilogarithms 23 195 204 205 Common antilogarithms, sample problems involving 195 Common antilogarithms, table of 204 205 Common logarithms 23 194 202 203 Common logarithms, computations using 196 Common logarithms, sample problems involving 194 Common logarithms, table of 202 203 Commutative law for dot products 118 Commutative law for vector addition 117 Complement 20 Complementary error function 183 Complex conjugate 21 Complex inversion formula 161 complex numbers 21 22 25 Complex numbers, addition of 21 Complex numbers, amplitude of 22 Complex numbers, conjugate 21 Complex numbers, definitions involving 21 Complex numbers, division of 21 25 Complex numbers, graphs of 22 Complex numbers, imaginary part of 21 Complex numbers, logarithms of 25 Complex numbers, modulus of 22 Complex numbers, multiplication of 21 25 Complex numbers, polar form of 22 25 Complex numbers, real part of 21 Complex numbers, roots of 22 25 Complex numbers, subtraction of 21 Complex numbers, vector representation of 22 Component vectors 117 Components of a vector 117 Compound amount, table of 240 Cone, elliptic 51 Confocal ellipses 127 Confocal ellipses, ellipsoidal coordinates 130 Confocal ellipses, hyperbolas 127 Confocal ellipses, parabolas 126 Confocal ellipses, paraboloidal coordinates 130 Conical coordinates 129 Conical coordinates, Laplacian in 129 Conies 37 (see also “Ellipse” “Parabola” “Hyperbola”) Conjugate, complex 21 Constant of integration 57 Convergence factors, table of 192 Convergence of Fourier series 131 Convergence, interval of 110 Coordinate curves 124 Coordinate system 11 Coordinates spherical 50 126 Coordinates, curvilinear 124—130 Coordinates, cylindrical 49 126 Coordinates, polar 22 36 Coordinates, rectangular 36 117 Coordinates, rotation of 36 49 Coordinates, special orthogonal 126—130 Coordinates, transformation of 36 48 49 Coordinates, translation of 36 49 Cosine integral 184 Cosine integral, Fresnel 184 Cosine integral, table of values for 251 Cosines, law of for plane triangles 19 Cosines, law of for spherical triangles 19 Counterclockwise 11 Cross or vector product 118 Cube roots, table of 238 239 Cube, duplication of 45 Cubes, table of 238 239 Cubic equation, solution of 32 Curl 120 Curl in curvilinear coordinates 125 Curtate cycloid 42 Curves, coordinate 124 Curves, special plane 40—45 Curvilinear coordinates 124 125 Curvilinear coordinates, orthogonal 124—130 Cycloid 40 42 Cycloid, curtate 42 Cycloid, prolate 42 Cylinder, elliptic 51 Cylinder, lateral surface area of 8 9 Cylinder, volume of 8 9 Cylindrical coordinates 49 126 Cylindrical coordinates, Laplacian in 126 Definite integrals 94—100 Definite integrals, approximate formulas for 95 Definite integrals, definition of 94 Definite integrals, general formulas involving 94 95 Definite integrals, table of 95—100 DEGREES 1 199 200 Degrees, conversion of to radians 199 200 223 Degrees, relationship of to radians 12 199 200 Del operator 119 Del operator, miscellaneous formulas involving 120 Delta function 170 DeMoivre's theorem 22 25 derivatives 53—56 (see also “Differentiation”) Derivatives of elliptic functions 181 Derivatives of exponential and logarithmic functions 54 Derivatives of hyperbolic and inverse hyperbolic functions 54 55 Derivatives of trigonometric and inverse trigonometric functions 54 Derivatives of vectors 119 Derivatives, anti- 57 Derivatives, chain rule for 53 Derivatives, definition of 53 Derivatives, higher 55 Derivatives, partial 56 Descartes, folium of 43 Differential equations, solutions of basic 104-106 Differentials 55 Differentials of integrals 95 Differentials, rules for 56 Differentiation 53 (see also “Derivatives”) Differentiation, general rules for 53 Diocles cissoid of 45 Direction cosines 46 47 Direction numbers 46 48 Directrix 37 Discriminant 32 Distance between two points in a plane 34 Distance between two points in space 46 Distance from a point to a line 35 Distance from a point to a plane 48 Distributions, probability 189 Distributive law 117 Distributive law for dot products 118 Divergence 119 Divergence in curvilinear coordinates 125 Divergence theorem 123 Dot or scalar product 117 118 Double angle formulas for hyperbolic functions 27 Double angle formulas for trigonometric functions 16 Double integrals 122 Duplication formula for gamma functions 102 Duplication of cube 45 Eccentricity of ellipse 38 Eccentricity of hyperbola 39 Eccentricity of parabola 37 Eccentricity, definition of 37 ellipse 7 37 38 Ellipse, area of 7 Ellipse, eccentricity of 38 Ellipse, equation of 37 38 Ellipse, evolute of 44 Ellipse, focus of 38 Ellipse, perimeter of 7 Ellipse, semi-major and-minor axes of 7 38 Ellipses, confocal 127 Ellipsoid, equation of 51 Ellipsoid, volume of 10 Elliptic cone 51 Elliptic cylinder 51 Elliptic cylindrical coordinates 127 Elliptic cylindrical coordinates, Laplacian in 127 Elliptic functions 179—182 (see also “Elliptic integrals”) Elliptic functions, addition formulas for 180 Elliptic functions, derivatives of 181 Elliptic functions, identities involving 181 Elliptic functions, integrals of 182 Elliptic functions, Jacobi's 180 Elliptic functions, periods of 181 Elliptic functions, series expansions for 181 Elliptic functions, special values of 182 Elliptic integrals 179 180 Elliptic integrals of the first kind 179 Elliptic integrals of the second kind 179 Elliptic integrals of the third kind 179 180 Elliptic integrals, amplitude of 179 Elliptic integrals, Landen's transformation for 180 Elliptic integrals, Legendre's relation for 182 Elliptic integrals, table of values for 254 255 Elliptic paraboloid 52 Envelope 44 Epicycloid 42 Equation of line 34 Equation of line in parametric form 47 Equation of line in standard form 47 Equation of line perpendicular to plane 48 Equation of line, general 35 Equation of line, intercept form for 34 Equation of line, normal form for 35
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