Transactions of the Cambridge Philosophical Society, المجلد 22University Press, 1923 |
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الصفحة 16
... equation ( 8 ) below with Part v . of Barnes ' memoir ( loc . cit . ) shews that , in the special case when the expansion for ø ( s / a ) is not asymptotic but con- vergent , the asymptotic expansion of the function ƒ ( x ) can easily ...
... equation ( 8 ) below with Part v . of Barnes ' memoir ( loc . cit . ) shews that , in the special case when the expansion for ø ( s / a ) is not asymptotic but con- vergent , the asymptotic expansion of the function ƒ ( x ) can easily ...
الصفحة 23
... integral - π sin { ( q − a ) πs } $ ( s ) .egs 1 1 : Σπί Jp sm ( ars ) ... integral I , converges if where { sin y log - cos y arg 2 } | < πA + π COS Y - π ( q cos y - A ) ......... ( 7a ) ... equation as n DEFINED BY TAYLOR'S SERIES . 23.
... integral - π sin { ( q − a ) πs } $ ( s ) .egs 1 1 : Σπί Jp sm ( ars ) ... integral I , converges if where { sin y log - cos y arg 2 } | < πA + π COS Y - π ( q cos y - A ) ......... ( 7a ) ... equation as n DEFINED BY TAYLOR'S SERIES . 23.
الصفحة 24
... ( 1 − x ) ] 3 − 1 ( 1 − x ) 3 — m − 1 = ( − x ) 3 – 1 mcn ( -x ) " , n = 0 and 0 + h + 1 while v is any fixed integer . . ( 10 ) We shall also shew that when arg ( − y 24 MR WATSON , ON A CLASS OF INTEGRAL FUNCTIONS.
... ( 1 − x ) ] 3 − 1 ( 1 − x ) 3 — m − 1 = ( − x ) 3 – 1 mcn ( -x ) " , n = 0 and 0 + h + 1 while v is any fixed integer . . ( 10 ) We shall also shew that when arg ( − y 24 MR WATSON , ON A CLASS OF INTEGRAL FUNCTIONS.
الصفحة 26
... equation ( 8 ) we see that if one or more of the numbers arg 2+ arg ( exp ( 2πiμ / a ) } | - ( μ = p , 1 - p , 2 − p , -- -- ... + p ) is less than , and if none are greater than , the asymptotic expansion of ƒ ( x ) is given by the ...
... equation ( 8 ) we see that if one or more of the numbers arg 2+ arg ( exp ( 2πiμ / a ) } | - ( μ = p , 1 - p , 2 − p , -- -- ... + p ) is less than , and if none are greater than , the asymptotic expansion of ƒ ( x ) is given by the ...
الصفحة 27
... integral along E is 0 ( zh ) . If , however , h , could not exceed some definite value , we should not get a ... equation of the form ƒ ( x ) = 0 ( | x | 11 ) , where is determinate ; this follows without difficulty from ( 10 ) . ( C ) ...
... integral along E is 0 ( zh ) . If , however , h , could not exceed some definite value , we should not get a ... equation of the form ƒ ( x ) = 0 ( | x | 11 ) , where is determinate ; this follows without difficulty from ( 10 ) . ( C ) ...
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a₁ angle approximately asymptotic expansion atmosphere Axiom of Archimedes axis b₁ c₁ calculated coefficients considered constant convergent convex set cordon corresponding cos² curve d₁ definition denote density determined differential equations disturbance diurnal diurnal variations dyadic earth equal escape expression factor finite follows formula free path function G. H. Hardy giant star given h₂ Hence integral equation invariant Jacobian k₁ k₂ magnitude molecules obtained orbit paper parameters partitions plane positive potential Primitive Roots ratio relation respectively result rotation scalar shew shewn sin² solar solid angle solutions substitution suppose surface t₁ theorem theory v₁ values vector velocity w₁ X₁ XXII zero Σ Σ дх