## Linear Operators: Spectral theory |

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Page 1527

The same process applied to the hypergeometric

z ) satisfies the confluent hypergeometric

dz dz2 This

The same process applied to the hypergeometric

**equation**[ 1 ] shows that ( a , y ;z ) satisfies the confluent hypergeometric

**equation**d2 [ 7 ] d 0+ ( y - 2 ) φ– αφ = 0 .dz dz2 This

**equation**has singularities at zero and infinity . The singularity at ...Page 1528

The first of these algebraic

of the differential

differential

irregular ...

The first of these algebraic

**equations**, which is simply the characteristic**equation**of the differential

**equation**, is quadratic ... f being a solution of the originaldifferential

**equation**Lt = 0 , we find that L'f ' has rational coefficients , and anirregular ...

Page 1529

The confluent hypergeometric

so that $ ( 1 ) = 0,5 ) = 1. Thus the Stokes lines for this

and negative imaginary axes . Trying solutions of the form z - 1 ( 1 + 02 + .

The confluent hypergeometric

**equation**has the characteristic**equation**a ? - = 0 ,so that $ ( 1 ) = 0,5 ) = 1. Thus the Stokes lines for this

**equation**are the positiveand negative imaginary axes . Trying solutions of the form z - 1 ( 1 + 02 + .

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