DLMF:1.12.E17
type: Item
DLMF defining formula: <math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1.1" class="ltx_Math" alttext="{\displaystyle{\displaystyle b_{0}+\cfrac{a_{1}}{b_{1}+\cfrac{a_{2}}{b_{2}+% \cfrac{a_{3}}{b_{3}+\cdots}}}={b_{0}+\cfrac{a_{1}/b_{1}}{1+\cfrac{a_{2}/(b_{1}% b_{2})}{1+\cfrac{a_{3}/(b_{2}b_{3})}{1+\cdots\cfrac{a_{n}/(b_{n-1}b_{n})}{1+% \cdots}}}}}={b_{0}+\cfrac{1}{(\ifrac{1}{a_{1}})b_{1}+\cfrac{1}{(\ifrac{a_{1}}{% a_{2}})b_{2}+\cfrac{1}{(\ifrac{a_{2}}{(a_{1}a_{3})})b_{3}+\cfrac{1}{(\ifrac{a_% {1}a_{3}}{(a_{2}a_{4})})b_{4}+\cdots}}}}}.}}" display="inline"> b 0 + a 1 b 1 + a 2 b 2 + a 3 b 3 + ⋯ = b 0 + a 1 / b 1 1 + a 2 / ( b 1 ⁢ b 2 ) 1 + a 3 / ( b 2 ⁢ b 3 ) 1 + ⋯ a n / ( b n - 1 ⁢ b n ) 1 + ⋯ = b 0 + 1 ( 1 / a 1 ) ⁢ b 1 + 1 ( a 1 / a 2 ) ⁢ b 2 + 1 ( a 2 / ( a 1 ⁢ a 3 ) ) ⁢ b 3 + 1 ( a 1 ⁢ a 3 / ( a 2 ⁢ a 4 ) ) ⁢ b 4 + ⋯ . <annotation-xml encoding="MathML-Content" id="p1.1.m1.1b"> <apply id="p1.1.m1.1.16.2.cmml" xref="p1.1.m1.1.16"> <and id="p1.1.m1.1.16.2a.cmml" xref="p1.1.m1.1.16"/> <apply id="p1.1.m1.1.16.2b.cmml" xref="p1.1.m1.1.16"> <eq id="p1.1.m1.1.5.cmml" xref="p1.1.m1.1.5"/> <apply id="p1.1.m1.1.16.2.2.cmml" xref="p1.1.m1.1.16.2.2"> <plus id="p1.1.m1.1.3.cmml" xref="p1.1.m1.1.3"/> <apply id="p1.1.m1.1.16.2.2.1.cmml" xref="p1.1.m1.1.16.2.2.1"> <csymbol cd="ambiguous" id="p1.1.m1.1.16.2.2.1.1.cmml" xref="p1.1.m1.1.16.2.2.1">subscript</csymbol> <ci id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">𝑏</ci> <cn type="integer" id="p1.1.m1.1.2.1.cmml" xref="p1.1.m1.1.2.1">0</cn> </apply> <apply id="p1.1.m1.1.4.cmml" xref="p1.1.m1.1.4"> <csymbol cd="latexml" id="p1.1.m1.1.4.1.cmml" xref="p1.1.m1.1.4">continued-fraction</csymbol> <apply id="p1.1.m1.1.4.2.cmml" xref="p1.1.m1.1.4.2"> <csymbol cd="ambiguous" id="p1.1.m1.1.4.2.3.cmml" xref="p1.1.m1.1.4.2">subscript</csymbol> <ci id="p1.1.m1.1.4.2.1.cmml" xref="p1.1.m1.1.4.2.1">𝑎</ci> <cn type="integer" id="p1.1.m1.1.4.2.2.1.cmml" xref="p1.1.m1.1.4.2.2.1">1</cn> </apply> <apply id="p1.1.m1.1.4.3.cmml" xref="p1.1.m1.1.4"> <plus id="p1.1.m1.1.4.3…
comment: Warning: Falling back to standard tex;
Digital Library of Mathematical Functions ID: 1.12.E17
Symbols used: nonnegative integer
instance of: Digital Library of Mathematical Functions Formula
MaRDI profile type: MaRDI formula profile