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classification of parameters

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1: 31.2 Differential Equations
All other homogeneous linear differential equations of the second order having four regular singularities in the extended complex plane, { } , can be transformed into (31.2.1). …
2: 31.14 General Fuchsian Equation
α β = j = 1 N a j q j .
3: 2.8 Differential Equations with a Parameter
§2.8(i) Classification of Cases
4: 18.27 q -Hahn Class
A (nonexhaustive) classification of such systems of OP’s was made by Hahn (1949). …These families depend on further parameters, in addition to q . The generic (top level) cases are the q -Hahn polynomials and the big q -Jacobi polynomials, each of which depends on three further parameters. … Some of the systems of OP’s that occur in the classification do not have a unique orthogonality property. …
5: 16.21 Differential Equation
16.21.1 ( ( - 1 ) p - m - n z ( ϑ - a 1 + 1 ) ( ϑ - a p + 1 ) - ( ϑ - b 1 ) ( ϑ - b q ) ) w = 0 ,
With the classification of §16.8(i), when p < q the only singularities of (16.21.1) are a regular singularity at z = 0 and an irregular singularity at z = . …
6: 16.4 Argument Unity
§16.4(i) Classification
The last condition is equivalent to the sum of the top parameters plus 2 equals the sum of the bottom parameters, that is, the series is 2-balanced. … The function F 2 3 ( a , b , c ; d , e ; 1 ) is analytic in the parameters a , b , c , d , e when its series expansion converges and the bottom parameters are not negative integers or zero. … These series contain 6 j symbols as special cases when the parameters are integers; compare §34.4. … Contiguous balanced series have parameters shifted by an integer but still balanced. …
7: 31.12 Confluent Forms of Heun’s Equation
31.12.1 d 2 w d z 2 + ( γ z + δ z - 1 + ϵ ) d w d z + α z - q z ( z - 1 ) w = 0 .
31.12.2 d 2 w d z 2 + ( δ z 2 + γ z + 1 ) d w d z + α z - q z 2 w = 0 .
31.12.3 d 2 w d z 2 - ( γ z + δ + z ) d w d z + α z - q z w = 0 .
31.12.4 d 2 w d z 2 + ( γ + z ) z d w d z + ( α z - q ) w = 0 .
8: 16.8 Differential Equations
§16.8(i) Classification of Singularities
16.8.3 ( ϑ ( ϑ + b 1 - 1 ) ( ϑ + b q - 1 ) - z ( ϑ + a 1 ) ( ϑ + a p ) ) w = 0 .