Download PDF by H. F. Baker: An Introduction To The Theory Of Multiply Periodic Functions

By H. F. Baker

ISBN-10: 1418167037

ISBN-13: 9781418167035

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P* i }a 2y f=f(x), . ' *-/(*), ,,*>-[* y Ja . y and F(x, z) We = 2X + shall \, (a; + z) + xz [2X, + X ,.. z*. }, 4 y < [* F- left side in (-) ' the identity shews that -R*'*, as a function an elementary integral of the third kind with logarithmic infinities ART. 6] connecting the integrals. 22 , are subject to the relation this leads to ; ,a + 2 ^a e r g u,', u rx - a = II*'" - [(z, \" Jo Now first let (z) s in the limit of - -=- 8 UA/ the limit of - I - (z, a)] dz. be in the neighbourhood of a particular place (z ), and express terms of the parameter of this place, and equate coefficients of the e power of this parameter; from uf> we obtain an expression which is and z x) [(z, x) ^ (z, a)] when t = 0; this we denote by which we denote by from p, (za ); u' c we *'" fj^(z ); dz we obtain the limit '" from IT*'" we obtain F^'"; from = for of [(z, x) (z, a)] -jj, is a certain rational function of (x) ; replacing now again which dt < .

6] connecting the integrals. 22 , are subject to the relation this leads to ; ,a + 2 ^a e r g u,', u rx - a = II*'" - [(z, \" Jo Now first let (z) s in the limit of - -=- 8 UA/ the limit of - I - (z, a)] dz. be in the neighbourhood of a particular place (z ), and express terms of the parameter of this place, and equate coefficients of the e power of this parameter; from uf> we obtain an expression which is and z x) [(z, x) ^ (z, a)] when t = 0; this we denote by which we denote by from p, (za ); u' c we *'" fj^(z ); dz we obtain the limit '" from IT*'" we obtain F^'"; from = for of [(z, x) (z, a)] -jj, is a certain rational function of (x) ; replacing now again which dt < .

Cuts where <*>'=/(); drawn through an arbitrary point of these formulae a space, give parametric representation of the surface tu = as a chord of the space cubic can be in terms of two arbitrary parameters Further, it is & (f & ) when (f, iy', f, . not difficult to verify that the equation ( ^ (f) Q(f) + Q. , find where , 4 ~ = J [^ (^, ) 2*] (^ - )~* ", the cone has therefore the form and this, compared with xQ metric expression for It will means t + yQ + zQ + P = 0, be found that the surface of 3 3 t gives the preceding para- A = 0, = is also represented parametrically by CHAPTER II.

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An Introduction To The Theory Of Multiply Periodic Functions by H. F. Baker


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