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 WhittakerM

 http://functions.wolfram.com/07.44.16.0005.01

 Input Form

 WhittakerM[\[Nu], \[Mu], c z] WhittakerM[\[Lambda], \[Gamma], d z] == ((c z)^(1/2 + \[Mu]) (d z)^(1/2 + \[Gamma]) Sum[z^k Subscript[c, k], {k, 0, Infinity}])/E^((1/2) (c + d) z) /; Subscript[c, k] == ((d^k Pochhammer[1/2 + \[Gamma] - \[Lambda], k])/ (k! Pochhammer[1 + 2 \[Gamma], k])) HypergeometricPFQ[ {-k, -k - 2 \[Gamma], 1/2 + \[Mu] - \[Nu]}, {1/2 - k - \[Gamma] + \[Lambda], 1 + 2 \[Mu]}, -(c/d)] || Subscript[c, k] == ((c^k Pochhammer[1/2 + \[Mu] - \[Nu], k])/ (k! Pochhammer[1 + 2 \[Mu], k])) HypergeometricPFQ[ {-k, -k - 2 \[Mu], 1/2 + \[Gamma] - \[Lambda]}, {1/2 - k - \[Mu] + \[Nu], 1 + 2 \[Gamma]}, -(d/c)]

 Standard Form

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 MathML Form

 M TagBox["M", WhittakerM] ν , μ ( c z ) M TagBox["M", WhittakerM] λ , γ ( d z ) - c + d 2 z ( c z ) μ + 1 2 ( d z ) γ + 1 2 k = 0 z k c k /; c k d k ( γ - λ + 1 2 ) k TagBox[SubscriptBox[RowBox[List["(", RowBox[List["\[Gamma]", "-", "\[Lambda]", "+", FractionBox["1", "2"]]], ")"]], "k"], Pochhammer] k ! ( 2 γ + 1 ) k TagBox[SubscriptBox[RowBox[List["(", RowBox[List[RowBox[List["2", " ", "\[Gamma]"]], "+", "1"]], ")"]], "k"], Pochhammer] 3 F 2 ( - k , - k - 2 γ , μ - ν + 1 2 ; - k - γ + λ + 1 2 , 2 μ + 1 ; - c d ) TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "3"], SubscriptBox["F", "2"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[RowBox[List["-", "k"]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List[RowBox[List["-", "k"]], "-", RowBox[List["2", " ", "\[Gamma]"]]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List["\[Mu]", "-", "\[Nu]", "+", FractionBox["1", "2"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[RowBox[List[TagBox[RowBox[List[RowBox[List["-", "k"]], "-", "\[Gamma]", "+", "\[Lambda]", "+", FractionBox["1", "2"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List[RowBox[List["2", " ", "\[Mu]"]], "+", "1"]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[RowBox[List["-", FractionBox["c", "d"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False], Rule[Selectable, False]] c k c k ( μ - ν + 1 2 ) k TagBox[SubscriptBox[RowBox[List["(", RowBox[List["\[Mu]", "-", "\[Nu]", "+", FractionBox["1", "2"]]], ")"]], "k"], Pochhammer] k ! ( 2 μ + 1 ) k TagBox[SubscriptBox[RowBox[List["(", RowBox[List[RowBox[List["2", " ", "\[Mu]"]], "+", "1"]], ")"]], "k"], Pochhammer] 3 F 2 ( - k , - k - 2 μ , γ - λ + 1 2 ; - k - μ + ν + 1 2 , 2 γ + 1 ; - d c ) TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "3"], SubscriptBox["F", "2"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[RowBox[List["-", "k"]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List[RowBox[List["-", "k"]], "-", RowBox[List["2", " ", "\[Mu]"]]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List["\[Gamma]", "-", "\[Lambda]", "+", FractionBox["1", "2"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[RowBox[List[TagBox[RowBox[List[RowBox[List["-", "k"]], "-", "\[Mu]", "+", "\[Nu]", "+", FractionBox["1", "2"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List[RowBox[List["2", " ", "\[Gamma]"]], "+", "1"]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[RowBox[List["-", FractionBox["d", "c"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False], Rule[Selectable, False]] Condition WhittakerM ν μ c z WhittakerM λ γ d z -1 c d 2 -1 z c z μ 1 2 d z γ 1 2 k 0 z k Subscript c k Subscript c k d k Pochhammer γ -1 λ 1 2 k k Pochhammer 2 γ 1 k -1 HypergeometricPFQ -1 k -1 k -1 2 γ μ -1 ν 1 2 -1 k -1 γ λ 1 2 2 μ 1 -1 c d -1 Subscript c k c k Pochhammer μ -1 ν 1 2 k k Pochhammer 2 μ 1 k -1 HypergeometricPFQ -1 k -1 k -1 2 μ γ -1 λ 1 2 -1 k -1 μ ν 1 2 2 γ 1 -1 d c -1 [/itex]

 Rule Form

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 Date Added to functions.wolfram.com (modification date)

 2007-05-02