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Smithells Metals Reference Book by E.A. Brandes and G.B. Brook (Eds.)

By E.A. Brandes and G.B. Brook (Eds.)

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A + {n-l)d S n= - [ 2 a + ( n - l K ] 2 where S„ denotes the sum to η terms. GEOMETRIC PROGRESSION a, ar, a r 2 ... ar" 0(1-0 û(r"-l) " = (r-1) _ 1 = (1-r) where S„ denotes the sum to η terms. If a 2 r < 1 and n->oo, S ~ = (1-r) TAYLOR'S SERIES 2 (x-a) ( * ) + — W f(x) = f(a) + (x-af 3 (x-a) + — ^ j — Γ " (a) + . MACLAURIN'S SERIES 2 3 x x f(x) = f(0) + xf(0) + - f " ( 0 ) + - r ( 0 ) + . . In the following series, the region of convergence is indicated in parentheses. If n o region is shown, the series is convergent for all values of x.

P, qy r ... are constants) 2 Particular solution y = A + Bx + C x + . . If C φ 0, Ρ and j ; are of the same degree. dy If C = 0, Ρ and — are of the same degree, dx mx (c) P = k Q mx Particular solution y=A e m cj mx If e mxis a term of the complementary function, try y = Ax 2e mx If χ e is a term of the complementary function, try y = Ax e . (d) Ρ = I sin nx + m cos nx (/ and m constants, or zero) Particular solution y = A sin nx-\-B cos nx If C sin nx + D cos nx is a term of the complementary function try Ax sin nx + Bx cos Note: The constants A.

However, in view of the m u c h greater familiarity with À, a n d the very simple conversion factor, in this edition the Angstrom unit is used unless the c o n t r a r y is stated. 3975 Wavelength in  WAVELENGTHS, EXCITATION POTENTIALS, AND β FILTERS FREQUENTLY USED CRYSTALLOGRAPH1C WORK ß-filter Target Element Atomic No. 1 analysis of metallic materials WAVELENGTHS, EXCITATION POTENTIALS, A N D β FILTERS FREQUENTLY USED IN C R Y S T A L L O G R A P H I C WORK—continued Target ß-filter Material content Element Mass absorption Absorption coefficient edge μ-ρ gem Atomic No.

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