Oldham K., Spanier J. — The fractional Calculus: Theory and applications of differentiation and integration to arbitrary order :: Электронная библиотека попечительского совета мехмата МГУ

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Oldham K., Spanier J. — The fractional Calculus: Theory and applications of differentiation and integration to arbitrary order

$Oldham K., Spanier J. — The fractional Calculus: Theory and applications of differentiation and integration to arbitrary order$

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Название: The fractional Calculus: Theory and applications of differentiation and integration to arbitrary order

Авторы: Oldham K., Spanier J.

Аннотация:

The concept of differentiation and integration to noninteger order is by no means new. Interest in this subject was evident almost as soon as the ideas of the classical calculus were known—Leibniz (1859) mentions it in a letter to L'Hospital in 1695.1 The earliest more or less systematic studies seem to have been made in the beginning and middle of the 19th century by Liouville (1832a), Riemann (1953), and Holmgren (1864), although Euler (1730), Lagrange (1772), and others made contributions even earlier.

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Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1974

Количество страниц: 234

Добавлена в каталог: 06.12.2009

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Предметный указатель

Semidifferential equations, used to relate ground-level pollution concentrations to pollution generation rate      208
Semidifferentiation      14
Semidifferentiation and semiintegration, analog circuits for      148—154
Semidifferentiation, used to relate surface temperature to heat flux      203
Semiintegral electroanalysis      204
Semiintegrals      16 185 see
Semiintegrating circuits      152
Semiintegrating circuits, accuracy of      149
Shermergor, T.D.      2 222
Shilov, G.E.      13
Shinbrot, M.      12 14
Sine integrals      128
Sine integrals as hypergeometrics of complexity $\frac{1}{3}$       165
Sine integrals as reducible transcendentals      161
Sines and Cosines      see "Hyperbolic sines"
Sines and cosines as periodic functions, differintegration of      110
Sines and cosines of $\sqrt{x}$ , as hypergeometrics      161 163
Sines and cosines of $\sqrt{x}$ , as hypergeometrics, differintegration of      96
Sines and cosines, differintegration as examples of cyclo-differential functions      110—112
Sines and cosines, semiderivatives and semiintegrals      124—126
Sneddon, I.N.      12 13
Somorjai, R.L.      2 14 222
Spanier, J.      2 14 15 200 204 222
Special functions of mathematical physics, as K=L-2 transcendentals      177
Special functions of mathematical physics, interrelations among      79 81
Stegun, I.A.      219
Stephens, E.      10
Stirling numbers of first kind      19
Stirling numbers of first kind, table of values      18
Stirling numbers of second kind      22 37 81
Stirling numbers of second kind, notation for      15
Stirling numbers of second kind, table of values      22
Struve functions      124 125 177—178
Struve functions as hypergeometrics of complexity $\frac{0}{2}$       164
Struve functions as reducible transcendentals      161
Struve functions, notation for      15
Stuloff, N.      12
Symbolic methods      2
Synthesis diagrams      169
Synthesis diagrams for associated Legendre functions      173
Synthesis diagrams for K=L transcendentals      172—174
Synthesis diagrams for K=L-1 transcendentals      175—176
Synthesis diagrams for K=L-2 transcendentals      177—180
Synthesis diagrams Legend re line      173
Synthesis diagrams logarithm line      175
Synthesis diagrams, Bessel — Struve line      178
Synthesis diagrams, example illustrating principles      170

Synthesis diagrams, involving steps of $\frac{1}{3}$ and $\frac{1}{4}$       179—180
Tautochrone      2 4 5 183
Tautochrone problem, solution as a semiintegral      185
Tautochrone, coordinate system for      184
Tautochrone, equations for      185
Taylor's series      14 15
Techniques in fractional calculus      133—160
Terentev, N.M.      209 220
Term-by-term differentiation      38 74—75
Term-by-term differintegration      69—75
Term-by-term differintegration of arbitrary differintegrable series      71—74
Term-by-term differintegration, to negative order      71—72
Term-by-term differintegration, to positive order      74—75
Term-by-term integration      38
Titchmarsh, E.C.      79 222
Transcendental functions, interrelationships among      167
Transcendental functions, representation as hypergeometrics      162—165
Transcendental functions, representations of      161—180
Transmission line, impedance of      212 213
Transmission line, optimum termination of      212
Transmission line, simulation by discrete components      216
Transmission line, symbolism, diagram explaining      211
Transmission line, terminations, diagram depicting four alternatives      214
Transmission line, theory      2
Transport in semiinfinite medium      198—200
Transport problems      2
Transport theory      197
Tricomi, F.G.      220
Veinoglu, B.C.      222
von Wolfersdorf, L.      13
Wall, H.S.      153 223
Wallis' infinite product for $\pi$       3
Wallis, J.      3
Wastchenxo, Z.      7
Watanabe, Y.      10 79 223
Wave equation      11
Weakly singular intergral equation      see "Abel's integral equation"
Wetland, G.V.      13
Weyl differintegrals      95
Weyl integral      53
Weyl, H.      2 8 10 53 95 223
Widder, D.V.      11 38 223
Wiener, N.      2 223
Withers, R.F.J.      220
Young, L.C.      11
Zero, differintegration of      63
Zeta function      142—143
Zygmund, A.      10 11 14

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