3 I2 



INDEX 



E PAGE 



Ellipse 46 



Ellipsoidal coordinates 102 



Elliptic cylinder coordinates 104 



Elliptic integrals, first kind 245 



second kind . 248 



third kind 251 



Elliptic integral expansions 135, 195 



Envelope 40 



Envelope of surfaces 56 



Epicycloid 52 



Equations, algebraic 2 



transcendental, roots of 84 



Equiangular spiral 53 



Eta functions 251 



Euler's constant 27 



summation formula 25 



transformation formula 113 



theorem for homogeneous functions. 157 



Eulerian angles 32 



Evolute 39 



Exact differential equations 163, 177 



Expansion of determinants 13 



Expansion theorem, Bromwich's 212 



Heaviside's 212 



PAGE 

 Homogeneous differential equations 



162, 166, 177 



Homogeneous linear equations 15 



Homer's method 7 



^Hospital's rule. 145 



Hyperbola 48 



Hyperbolic functions 71 



spiral 52 



Hypergeometric differential equation 209 



series 209 



Hypergeometric function, confluent. . . 185 



Hypocycloid 52 



Identities, algebraic i 



Implicit functions, derivatives of 161 



Indeterminate forms 145 



Indicial equation 174 



Infinite products 130 



series 109 



Integrating factors 163 



Interpolation formula, Newton's 22 



Intrinsic equation of plane curves. ... 44 



Involute of plane curves 39 



Finite differences and sums 



Finite products of circular functions. 



Finite series, special 



Fourier's series 



Fresnel's integrals 



Functional determinants. . 



20 



84 



26 



136 



134 



16 



Jacobian 16 



K 



Ker and Kei functions 205 



Rummer's transformation 114 



Gamma function 



Gauss's II function .... 



theorem 



Geometrical progressions . 



Gradient of vector 



Graeffe's method 



Green's theorem 



Gregory's series 



Gudermannian. . 



H 



Harmonical progressions 



Harmonics, zonal 



Heaviside's operational methods. 



expansion theorem 



Helical coordinates 



Hessian. . 



133 

 95 

 26 



93 



8 



95 



122 



76 



26 

 191 

 210 

 212 



106 

 16 



Lagrange's theorem 112 



Laplace's integrals 193 



Latus rectum, ellipse 48 



hyperbola 49 



parabola 46 



Leclert's transformation. ^ 115 



Legendre's equation 191 



Leibnitz's theorem 157 



Lemniscate 53 



Limiting values of products 152 



sums 151 



Linear equations 15 



Linear vector function 96 



Lituus 53 



Logarithmic spiral 53 



M 



Maclaurin's theorem 112 



Markoff's transformation formula. ... 113 



