relation to Kummer equation
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1: 13.14 Definitions and Basic Properties
2: 13.2 Definitions and Basic Properties
3: 13.6 Relations to Other Functions
§13.6(i) Elementary Functions
… โบ§13.6(ii) Incomplete Gamma Functions
… โบ§13.6(iv) Parabolic Cylinder Functions
… โบ§13.6(v) Orthogonal Polynomials
… โบ§13.6(vi) Generalized Hypergeometric Functions
…4: 13.3 Recurrence Relations and Derivatives
§13.3 Recurrence Relations and Derivatives
โบ§13.3(i) Recurrence Relations
… โบKummer’s differential equation (13.2.1) is equivalent to … โบ§13.3(ii) Differentiation Formulas
…5: 10.16 Relations to Other Functions
§10.16 Relations to Other Functions
โบElementary Functions
… โบParabolic Cylinder Functions
… โบConfluent Hypergeometric Functions
… โบGeneralized Hypergeometric Functions
…6: 10.39 Relations to Other Functions
§10.39 Relations to Other Functions
โบElementary Functions
… โบParabolic Cylinder Functions
… โบConfluent Hypergeometric Functions
… โบGeneralized Hypergeometric Functions and Hypergeometric Function
…7: 18.34 Bessel Polynomials
8: 13.29 Methods of Computation
§13.29(iv) Recurrence Relations
โบThe recurrence relations in §§13.3(i) and 13.15(i) can be used to compute the confluent hypergeometric functions in an efficient way. … โบnormalizing relation … โบnormalizing relation …9: Errata
The Kronecker delta symbols have been moved furthest to the right, as is common convention for orthogonality relations.
Following a suggestion from James McTavish on 2017-04-06, the recurrence relation was added to Equation (9.7.2).
A number of additions and changes have been made to the metadata to reflect new and changed references as well as to how some equations have been derived.
The equality has been added to the original equation to express an explicit connection between the two standard solutions of Kummer’s equation. Note also that the notation has been changed to .
Reported 2015-02-10 by Adri Olde Daalhuis.
The equality has been added to the original equation to express an explicit connection between the two standard solutions of Kummer’s equation.
Reported 2015-02-10 by Adri Olde Daalhuis.