Linear Operators: Spectral theory |
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Page 1433
а = is called the indicial equation of [ * ] at zero . If the indicial equation has distinct roots e , ... , en , no two of which differ by an integer , then the set of solutions of [ * ] has a basis of the form o , ( z ) = z'q ; ( ) ...
а = is called the indicial equation of [ * ] at zero . If the indicial equation has distinct roots e , ... , en , no two of which differ by an integer , then the set of solutions of [ * ] has a basis of the form o , ( z ) = z'q ; ( ) ...
Page 1527
The same process applied to the hypergeometric equation [ 1 ] shows that Øla , y ; 2 ) satisfies the confluent hypergeometric equation d2 [ 7 ] 2 ( ) d 0+ ( y - 2 ) --0-0 = 0 . dz dz2 -2 ) This equation has singularities at zero and ...
The same process applied to the hypergeometric equation [ 1 ] shows that Øla , y ; 2 ) satisfies the confluent hypergeometric equation d2 [ 7 ] 2 ( ) d 0+ ( y - 2 ) --0-0 = 0 . dz dz2 -2 ) This equation has singularities at zero and ...
Page 1529
The confluent hypergeometric equation has the characteristic equation a ? — Q = 0 , so that ( 1 ) 0 , so that 511 ) = 0 , $ 41 ) 1. Thus the Stokes lines for this equation are the positive and negative imaginary axes .
The confluent hypergeometric equation has the characteristic equation a ? — Q = 0 , so that ( 1 ) 0 , so that 511 ) = 0 , $ 41 ) 1. Thus the Stokes lines for this equation are the positive and negative imaginary axes .
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Contents
BAlgebras | 859 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
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