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| Авторизация |
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| Spiegel M.R. — Schaum's mathematical handbook of formulas and tables |
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| Предметный указатель |
Equation of line general 35
Equation of line in parametric form 47
Equation of line in standard form 47
Equation of line intercept form for 34
Equation of line normal form for 35
Equation of line perpendicular to plane 48
Equation of plane, general 47
Equation of plane, intercept form for 47
Equation of plane, normal form for 48
Equation of plane, passing through three points 47
Error function 183
Error function complementary 183
Error function table of values of 257
Euler numbers 114 115
Euler numbers definition of 114
Euler numbers relationship of, to Bernoulli numbers 115
Euler numbers series involving 115
Euler numbers table of first few 114
Euler or Cauchy differential equation 105
Euler — Maclaurin summation formula 109
Euler's constant 1
Euler's identities 24
Evolute of an ellipse 44
Exact differential equation 104
Exponential functions 23—25 200
Exponential functions, periodicity of 24
Exponential functions, relationship of to trigonometric functions 24
Exponential functions, sample problems involving calculation of 200
Exponential functions, series for 111
Exponential functions, table of 226 227
Exponential integral 183
Exponential integral table of values for 251
Exponents 23
F distribution 1899
F distribution 95th and 99th percentile values for 260 261
Factorial n 3
Factorial n, table of values for 234
Factors 2
Focus, of conic 37
Focus, of ellipse 38
Focus, of hyperbola 39
Focus, of parabola 38
Folium of Descartes 43
Fourier series 131—135
Fourier series, complex form of 131
Fourier series, convergence of 131
Fourier series, definition of 131
Fourier series, Parseval's identity for 131
Fourier series, special 132—135
Fourier transforms 174—178
Fourier transforms sine 175
Fourier transforms table of 176—178
Fourier transforms, convolution theorem for 175
Fourier transforms, cosine 176
Fourier transforms, definition of 175
Fourier transforms, Parseval's identity for 175
Fourier's integral theorem 174
Fresnel sine and cosine integrals 184
Frullani's integral 100
Frustrum of right circular cone, lateral surface area of 9
Frustrum of right circular cone, volume of 9
Gamma function 1 101 102
Gamma function asymptotic expansions for 102
Gamma function definition of 101 102
Gamma function derivatives of 102
Gamma function duplication formula for 102
Gamma function for negative values 101
Gamma function graph of 101
Gamma function infinite product for 102 188
Gamma function recursion formula for 101
Gamma function relationship of to beta function 103
Gamma function relationships involving 102
Gamma function special values for 101
Gamma function table of values for 235
Gauss' theorem 123
Gaussian plane 22
Generalized integration by parts 59
Generating functions 137 139 146 149 151 153 155 157 158
Geometric formulas 5—10
Geometric mean 185
Geometric series 107
Geometric series arithmetic- 107
Gradient 119
Gradient in curvilinear coordinates 125
Green's first and second identities 124
Green's theorem 123
Half angle formulas, for hyperbolic functions 27
Half angle formulas, for trigonometric functions 16
Half rectified sine wave function 172
Hankel functions 138
Harmonic mean 185
Heaviside's unit function 173
Hermite polynomials 151 152
Hermite polynomials addition formulas for 152
Hermite polynomials generating function for 151
Hermite polynomials orthogonal series for 152
Hermite polynomials orthogonality of 152
Hermite polynomials recurrence'formulas for 151
Hermite polynomials Rodrigue's formula for 151
Hermite polynomials special 151
Hermite polynomials special results involving 152
Hermite's differential equation 151
Higher derivatives 55
Higher derivatives Leibnitz rule for 55
Holder's inequality 185
Holder's inequality for integrals 186
Homogeneous differential equation 104
Homogeneous differential equation linear second order 105
Hyperbola 37 39
Hyperbola asymptotes of 39
Hyperbola eccentricity of 39
Hyperbola equation of 37
Hyperbola focus of 39
Hyperbola length of major and minor axes of 39
Hyperbolas, confocal 127
Hyperbolic functions 26—31
Hyperbolic functions addition formulas for 27
Hyperbolic functions definition of 26
Hyperbolic functions double angle formulas for 27
Hyperbolic functions graphs of 29
Hyperbolic functions half angle formulas for 27
Hyperbolic functions inverse see “Inverse hyperbolic functions”
Hyperbolic functions multiple angle formulas for 27
Hyperbolic functions of negative arguments 26
Hyperbolic functions periodicity of 31
Hyperbolic functions powers of 28
Hyperbolic functions relationship of to trigonometric functions 31
Hyperbolic functions relationships among 26 28
Hyperbolic functions sample problems for calculation of 200 201
Hyperbolic functions series for 112
Hyperbolic functions sum, difference and product of 28
Hyperbolic functions table of values for 228—233
Hyperbolic paraboloid 52
Hyperboloid, of one sheet 51
Hyperboloid, of two sheets 52
Hypergeometric differential equation 160
Hypergeometric differential equation distribution 189
Hypergeometric functions 160
Hypergeometric functions miscellaneous properties of 160
Hypergeometric functions special cases of 160
Hypocycloid, general 42
Hypocycloid, general with four cusps 40
Imaginary part of a complex number 21
Imaginary unit 21
Improper integrals 94
Indefinite integrals 57—93
Indefinite integrals definition of 57
Indefinite integrals table of 60—93
Indefinite integrals transformation of 59 60
Inequalities 185 186
| Infinite products 102 188
Infinite products series see “Series”
Initial point of a vector 116
Integral calculus, fundamental theorem of 94
Integrals, definite see “Definite integrals”
Integrals, double 122
Integrals, improper 94
Integrals, indefinite see “Indefinite integrals”
Integrals, involving vectors 121
Integrals, line see “Line integrals”
Integrals, multiple 122 125
Integration see also “Integrals” 57
Integration by parts 57
Integration by parts generalized 59
Integration constants of 57
Integration general rules of 57—59
Intercepts 34 47
Interest 201 240—243
Interpolation 195
Interval of convergence 110
Inverse hyperbolic functions 29—31
Inverse hyperbolic functions definition of 29
Inverse hyperbolic functions expressed in terms of logarithmic functions 29
Inverse hyperbolic functions graphs of 30
Inverse hyperbolic functions principal values for 29
Inverse hyperbolic functions relationship of to inverse trigonometric functions 31
Inverse hyperbolic functions relationships between 30
Inverse Laplace transforms 161
Inverse trigonometric functions 17—19
Inverse trigonometric functions definition of 17
Inverse trigonometric functions graphs of 18 19
Inverse trigonometric functions principal values for 17
Inverse trigonometric functions relations between 18
Inverse trigonometric functions relationship of to inverse hyperbolic functions 31
Involute of a circle 43
Jacobi's elliptic functions 180
Jacobian 125
Ker and Kei functions 140 141
Ker and Kei functions definition of 140
Ker and Kei functions differential equation for 141
Ker and Kei functions graphs of 141
Lagrange form of remainder in Taylor series 110
Laguerre polynomials 153 154
Laguerre polynomials associated see “Associated Laguerre polynomials”
Laguerre polynomials generating function for 153
Laguerre polynomials orthogonal series for 154
Laguerre polynomials orthogonality of 154
Laguerre polynomials recurrence formulas for 153
Laguerre polynomials Rodrigue's formula for 153
Laguerre polynomials special 153
Laguerre's associated differential equation 155
Laguerre's differential equation 153
Landen's transformation 180
Laplace transforms 161—173
Laplace transforms complex inversion formula for 161
Laplace transforms definition of 161
Laplace transforms inverse 161
Laplace transforms table of 162—173
Laplacian 120
Laplacian in curvilinear coordinates 125
Legendre functions see also “Legendre polynomials” 146—148
Legendre functions associated see “Associated Legendre functions”
Legendre functions of the second kind 148
Legendre polynomials see also “Legendre functions” 146 147
Legendre polynomials generating function for 146
Legendre polynomials orthogonal series of 147
Legendre polynomials orthogonality of 147
Legendre polynomials recurrence formulas for 147
Legendre polynomials Rodrigue's formula for 146
Legendre polynomials special 146
Legendre polynomials special results involving 147
Legendre polynomials table of values for 252 253
Legendre's associated differential equation 149
Legendre's associated differential equation general solution of 150
Legendre's differential equation 106 146
Legendre's differential equation general solution of 148
Legendre's relation for elliptic integrals 182
Leibnitz's rule, for differentiation of integrals 95
Leibnitz's rule, for higher derivatives of products 55
Lemniscate 40 44
Limacon of Pascal 41 44
Line integrals 121 122
Line integrals definition of 121
Line integrals independence of path of 121 122
Line integrals properties of 121
Line, equation of see “Equation of line”
Line, equation of integrals see “Line integrals”
Line, slope of 34
Linear first order differential equation 104
Linear second order differential equation 105
Logarithmic functions see also “Logarithms” 23—25
Logarithmic functions, series for 111
Logarithms see also “Logarithmic functions” 23
Logarithms base of 23
Logarithms Briggsian 23
Logarithms change of base of 24
Logarithms characteristic of 194
Logarithms common see “Common logarithms”
Logarithms mantissa of 194
Logarithms natural 24
Logarithms of trigonometric functions 216—221
Logarithms, antilogarithms and see “Antilogarithms”
Logarithms, of complex numbers 25
Maclaurin series 110
Mantissa 194
Mean value theorem, for definite integrals 94
Mean value theorem, generalized 95
Minkowski's inequality 186
Minkowski's inequality for integrals 186
Modified Bessel functions 138 139
Modified Bessel functions of order half an odd integer 140
Modified Bessel functions, differential equation for 138
Modified Bessel functions, generating function for 139
Modified Bessel functions, graphs of 141
Modified Bessel functions, recurrence formulas for 139
Modulus, of a complex number 22
Moments of inertia, special 190 191
Multinomial formula 4
Multiple angle formulas, for hyperbolic functions 27
Multiple angle formulas, for trigonometric functions 16
Multiple integrals 122
Multiple integrals, transformation of 125
Napier's rules 20
Napierian logarithms 24 196
Napierian logarithms, tables of 224 225
Natural logarithms and antilogarithms 24 196
Natural logarithms and antilogarithms, tables of 224—227
Neumann's function 136
Nonhomogeneous equation, linear second order 105
Normal curve, areas under 257
Normal curve, ordinates of 256
Normal distribution 189
Normal form, equation of line in 35
Normal form, equation of plane in 48
Normal, outward drawn or positive 123
Normal, outward drawn or positive unit 122
Null function 170
Null vector 116
Numbers, complex see “Complex numbers”
Oblate spheroidal coordinates 128
Oblate spheroidal coordinates, Laplacian in 128
Orthogonal curvilinear coordinates 124—130
Orthogonal curvilinear coordinates formulas involving 125
Orthogonality and orthogonal series 144 145 147 150 152 154 156 158 159
Ovals of Cassini 44
parabola 37 38
Parabola eccentricity of 37
Parabola equation of 37 38
Parabola focus of 38
Parabola segment of see “Segment of parabola”
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