A Course of Modern Analysis; An Introduction to the General Theory of Infinite Processes And of Analytic Functions; With An Account of the Principal Transcendental Functions
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In our eReader you can find the full English version of the book. Read A Course of Modern Analysis; An Introduction to the General Theory of Infinite Processes And of Analytic Functions; With An Account of the Principal Transcendental Functions Online - link to read the book on full screen. Our eReader also allows you to upload and read Pdf, Txt, ePub and fb2 books. In the Mini eReder on the page below you can quickly view all pages of the book - Read Book A Course of Modern Analysis; An Introduction to the General Theory of Infinite Processes And of Analytic Functions; With An Account of the Principal Transcendental Functions
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To quickly assess the difficulty of the text, read a short excerpt:
, du , is satisfied by the hypergeometric series of § 2 '38.
Obtain the complete solution of the equation when c = l.
104. Solutions valid for large values of\z\.
Let z=ljz 1 ; then a solution of the differential equation is said to be valid for ' large values of | z \ ' if it is valid for sufficiently small values of | z x \ ; and it is said that ' the point at infinity is an ordinary (or regular or irregular) point of the equation ' when the point z x = is an ordinary (or regular or irregular...) point of the equation when it has been transformed so that z x is the independent variable.
Since d?u , .du . . , d 2 u L „ . /1\) du (1\ ^ +P W s + q W » S * ^ + {*,■ - *tp (-)} T ^ + a (-) u, we see that the conditions that the point i = oo should be (i) an ordinary point, (ii) a regular point, are (i) that %z — z 2 p(z), z i q(z) should be analytic at infinity (§ 5'62) and (ii) that zp (z), z 2 q (z) should be analytic at infinity.
Example 1. Shew that every point (including infinity) is either an ordinary point or a regular point for each of the equations z(i - 3) S +{c_(a+6+i)2} S _a6a=o ' where a, b, c, n are constants.
What to read after A Course of Modern Analysis; An Introduction to the General Theory of Infinite Processes And of Analytic Functions; With An Account of the Principal Transcendental Functions?
You can find similar books in the "Read Also" column, or choose other free books by G N George Neville Watson to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
, du , is satisfied by the hypergeometric series of § 2 '38.
Obtain the complete solution of the equation when c = l.
104. Solutions valid for large values of\z\.
Let z=ljz 1 ; then a solution of the differential equation is said to be valid for ' large values of | z \ ' if it is valid for sufficiently small values of | z x \ ; and it is said that ' the point at infinity is an ordinary (or regular or irregular) point of the equation ' when the point z x = is an ordinary (or regular or irregular...) point of the equation when it has been transformed so that z x is the independent variable.
Since d?u , .du . . , d 2 u L „ . /1\) du (1\ ^ +P W s + q W » S * ^ + {*,■ - *tp (-)} T ^ + a (-) u, we see that the conditions that the point i = oo should be (i) an ordinary point, (ii) a regular point, are (i) that %z — z 2 p(z), z i q(z) should be analytic at infinity (§ 5'62) and (ii) that zp (z), z 2 q (z) should be analytic at infinity.
Example 1. Shew that every point (including infinity) is either an ordinary point or a regular point for each of the equations z(i - 3) S +{c_(a+6+i)2} S _a6a=o ' where a, b, c, n are constants.
What to read after A Course of Modern Analysis; An Introduction to the General Theory of Infinite Processes And of Analytic Functions; With An Account of the Principal Transcendental Functions?
You can find similar books in the "Read Also" column, or choose other free books by G N George Neville Watson to read onlineMoreLess
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