|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
http://functions.wolfram.com/01.05.06.0006.01
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Log[a, 1 + z] == (z/Log[a]) Hypergeometric2F1[1, 1, 2, -z]
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Cell[BoxData[RowBox[List[RowBox[List["Log", "[", RowBox[List["a", ",", RowBox[List["1", "+", "z"]]]], "]"]], "\[Equal]", RowBox[List[FractionBox["z", RowBox[List["Log", "[", "a", "]"]]], " ", RowBox[List["Hypergeometric2F1", "[", RowBox[List["1", ",", "1", ",", "2", ",", RowBox[List["-", "z"]]]], "]"]]]]]]]]
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <msub> <mi> log </mi> <mi> a </mi> </msub> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> + </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mrow> <mfrac> <mi> z </mi> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> a </mi> <mo> ) </mo> </mrow> </mfrac> <mo> ⁢ </mo> <semantics> <mrow> <mrow> <msub> <mo>   </mo> <mn> 2 </mn> </msub> <msub> <mi> F </mi> <mn> 1 </mn> </msub> </mrow> <mo> ⁡ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 1 </mn> <mo> , </mo> <mn> 1 </mn> </mrow> <mo> ; </mo> <mn> 2 </mn> <mo> ; </mo> <mrow> <mo> - </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["2", TraditionalForm]], SubscriptBox["F", FormBox["1", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox["1", Hypergeometric2F1, Rule[Editable, True]], ",", TagBox["1", Hypergeometric2F1, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1, Rule[Editable, False]], ";", TagBox[TagBox[TagBox["2", Hypergeometric2F1, Rule[Editable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1, Rule[Editable, False]], ";", TagBox[RowBox[List["-", "z"]], Hypergeometric2F1, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], Hypergeometric2F1] </annotation> </semantics> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <log /> <logbase> <ci> a </ci> </logbase> <apply> <plus /> <cn type='integer'> 1 </cn> <ci> z </ci> </apply> </apply> <apply> <times /> <apply> <times /> <ci> z </ci> <apply> <power /> <apply> <ln /> <ci> a </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <ci> Hypergeometric2F1 </ci> <cn type='integer'> 1 </cn> <cn type='integer'> 1 </cn> <cn type='integer'> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
|
|
|
|
|
|
|
|
|
|
| |
|
|
|
|
| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Log", "[", RowBox[List["a_", ",", RowBox[List["1", "+", "z_"]]]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["z", " ", RowBox[List["Hypergeometric2F1", "[", RowBox[List["1", ",", "1", ",", "2", ",", RowBox[List["-", "z"]]]], "]"]]]], RowBox[List["Log", "[", "a", "]"]]]]]]] |
|
|
|
|
|
|
|
|
|
|
Date Added to functions.wolfram.com (modification date)
|
|
|
|
|
|
|
|
|
|
|
|
|
|