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33 Coulomb FunctionsVariables r,Ο΅

Β§33.17 Recurrence Relations and Derivatives

β“˜
Keywords:
Coulomb functions: variables r,Ο΅, derivatives, recurrence relations
Notes:
See Seaton (2002a, Eqs. 77, 78, 82).
Referenced by:
Β§33.23(iv), Β§33.23(iv)
Permalink:
http://dlmf.nist.gov/33.17
See also:
Annotations for Ch.33
33.17.1 (β„“+1)⁒r⁒f⁑(Ο΅,β„“βˆ’1;r)βˆ’(2⁒ℓ+1)⁒(ℓ⁒(β„“+1)βˆ’r)⁒f⁑(Ο΅,β„“;r)+ℓ⁒(1+(β„“+1)2⁒ϡ)⁒r⁒f⁑(Ο΅,β„“+1;r)=0,
33.17.2 (β„“+1)⁒(1+β„“2⁒ϡ)⁒r⁒h⁑(Ο΅,β„“βˆ’1;r)βˆ’(2⁒ℓ+1)⁒(ℓ⁒(β„“+1)βˆ’r)⁒h⁑(Ο΅,β„“;r)+ℓ⁒r⁒h⁑(Ο΅,β„“+1;r)=0,
33.17.3 (β„“+1)⁒r⁒f′⁑(Ο΅,β„“;r) =((β„“+1)2βˆ’r)⁒f⁑(Ο΅,β„“;r)βˆ’(1+(β„“+1)2⁒ϡ)⁒r⁒f⁑(Ο΅,β„“+1;r),
33.17.4 (β„“+1)⁒r⁒h′⁑(Ο΅,β„“;r) =((β„“+1)2βˆ’r)⁒h⁑(Ο΅,β„“;r)βˆ’r⁒h⁑(Ο΅,β„“+1;r).
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