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" ... are to vanish with t. It has been proved that there are no regular integrals of the equation vanishing with t unless a is zero: and that, if a = 0, there exists a simple infinitude of regular integrals satisfying the equations. We proceed, not in... "
Memoirs Presented to the Cambridge Philosophical Society on the Occasion of ... - الصفحة 68
بواسطة Cambridge Philosophical Society - 1900 - عدد الصفحات: 447
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Theory of Differential Equations: (Vol. IV) Ordinary equations. 1902

Andrew Russell Forsyth - 1900 - عدد الصفحات: 405
...regular functions of their arguments of the same type as 6 and </> above, and the integrals ^ and t 2 are to vanish with t. It has been proved that there...t, these integrals being regular functions of t and tlogt: and when a is zero, these non-regular integrals do not exist. To establish this result, we proceed...

Transactions of the Cambridge Philosophical Society

Cambridge Philosophical Society - 1900 - عدد الصفحات: 530
...for positive integer values of X, p, v such that X + /t + v > 2, then the equations possess a double infinitude of non-regular integrals vanishing with t, these integrals being regular functions of t, t(>, if'. Immediate corollaries, when once this theorem is established, are as follows : — If the...

(vol. IV) Ordinary linear equations. 1902

Andrew Russell Forsyth - 1900 - عدد الصفحات: 416
...critical quadratic has its real part positive, and is not itself a positive integer, there is a double infinitude of non-regular integrals vanishing with t, these integrals being regular functions of t, tf, if log t. When the theorem is established, there is an immediate corollary : If the real part of...

Theory of Differential Equations, المجلد 3

Andrew Russell Forsyth - 1900 - عدد الصفحات: 414
...critical quadratic has its real part positive, and is not itself a positive integer, there is a double infinitude of non-regular integrals vanishing with t, these integrals being regular functions of t, <f , t* log t. When the theorem is established, there is an immediate corollary : If the real part...

Theory of Differential Equations

Andrew Russell Forsyth - 1969 - عدد الصفحات: 416
...critical quadratic has its real part positive, and is not itself a positive integer, there is a double infinitude of non-regular integrals vanishing with t, these integrals being regular functions of t, tf, t* logt. When the theorem is established, there is an immediate corollary : If the real part of...
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memoirs

عدد الصفحات: 530
...vanishes for positive integer values of \, p, v such that \ + n+v^2, then the equations possess a double infinitude of non-regular integrals vanishing with t, these integrals being regular functions of t, t^, t£*. Immediate corollaries, when once this theorem is established, are as follows : — If the...
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