M. Z. v. Krzywoblocki Sc. D. (Lille), Ph. D. (Brooklyn), M.'s Bergman’s Linear Integral Operator Method in the Theory of PDF

By M. Z. v. Krzywoblocki Sc. D. (Lille), Ph. D. (Brooklyn), M. A. (Math., Stanford), M. S. (Appl. Math., Brown) M. Aer. En. (Brooklyn), Dipl. Ing. (Lemberg) (auth.)

ISBN-10: 3709139945

ISBN-13: 9783709139943

ISBN-10: 3709139953

ISBN-13: 9783709139950

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Extra info for Bergman’s Linear Integral Operator Method in the Theory of Compressible Fluid Flow

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6) 45 4. ~:'). ~n) are given in 6, p. 269. )'/3 for k = 1·4. This choice yields T = e If these series are substituted in (1. 111 = 1. + + . t 4. 2) converges very slowly, and it is therefore necessary to employ a large number of terms in order to obtain a good approximation for T*. 7), the number m must be chosen rather large. If this is the case, it is then expedient to replace the expansion (1. 2) by (1. 9). Theoretically, this is, however, not the only way of overcoming this difficulty, and in the following other means of doing so will be indicated: this alternative approach employs the method of analytic continuation.

1) If we compute this last integral, we obtain an integration constant each time, since the lower limit is arbitrary, i. , Gn would depend on n constants of integration. 9, we choose as the lower limit of the integrals the value A = - =, corresponding to f = m = 0 (1. 3 . 11) and (1. 13). However, at A = 0 or m = 1, all Gn become infinite. It is therefore proper to select other functions r n in the place of the Gn which remain bounded (i. , finite). To find such rn one has to study the behavior of the G n near m = 1, or, what is the same, the behavior of f (T) and Gn (T) in a neighborhood of T = O.

1) 7J + Fo p* = 0, P: and its solution can be written in the form t p* ( 5, 'Yj = +1 )_ \{ - J cos 1=-1 ·1} tII [2 t (511)'/. Po . 2) where I and g are two arbitrary, twice-continuously differentiable functions of one variable. 2), the independent variables of functions I and [! 'Yj g should be substituted by the expressions [! 5 F O-1 (1 - t2)] and F 0 -1 (1 - t 2)], respectively. In many instances, it is necessary to have representations of the solutions which are valid in the whole strip - 00 < () < 00, < 2 A < 2 n (h-1 - 1), say.

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Bergman’s Linear Integral Operator Method in the Theory of Compressible Fluid Flow by M. Z. v. Krzywoblocki Sc. D. (Lille), Ph. D. (Brooklyn), M. A. (Math., Stanford), M. S. (Appl. Math., Brown) M. Aer. En. (Brooklyn), Dipl. Ing. (Lemberg) (auth.)


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