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  [[q-Fibonacci polynomials | $q$-Fibonacci polynomials]]<br /> ==Special functions in number theory==
  26 KB (2,938 words) - 15:47, 26 August 2023
• Q-Fibonacci polynomials
  The $q$-Fibonacci polynomials are defined by ...\neq 0$ is a function of a (real) variable $s$ and $q \neq 0$ is a [[real number]].
  773 bytes (129 words) - 07:25, 16 June 2016
• Fibonacci zeta function
  The Fibonacci zeta function is defined by where $F_n$ denotes the $n$th [[Fibonacci numbers|Fibonacci number]].
  704 bytes (99 words) - 00:25, 24 May 2017
• Reciprocal Fibonacci constant
  The reciprocal Fibonacci constant $\psi$ is where $F(k)$ is is the $k$th [[Fibonacci numbers|Fibonacci number]].
  582 bytes (75 words) - 03:40, 25 June 2017
• Fibonacci zeta at 1 is irrational
  ...Fibonacci constant]]) is an [[irrational number]], where $F$ denotes the [[Fibonacci zeta function]].
  234 bytes (28 words) - 17:37, 19 August 2016
• Book:Elena Deza/Figurate Numbers
  ::1.5 Amount of a given number in all polygonal numbers :4. Areas of number theory including figurate numbers
  2 KB (234 words) - 21:52, 21 June 2016
• Sum of Fibonacci numbers
  where $F_k$ denotes the $k$th [[Fibonacci numbers|Fibonacci number]]. * {{PaperReference|A Primer on the Fibonacci Sequence Part I|1963|S.L. Basin|author2=V.E. Hoggatt, Jr.|prev=Lucas number
  379 bytes (56 words) - 00:15, 25 May 2017
• Limit of quotient of consecutive Fibonacci numbers
  where $F(n)$ denotes the $n$th [[Fibonacci numbers|Fibonacci number]] and $\varphi$ denotes the [[golden ratio]]. ...res de Fibonacci|1899|Edmund Landau|prev=Fibonacci numbers|next=Reciprocal Fibonacci constant}}
  448 bytes (59 words) - 23:53, 6 June 2017
• Binet's formula
  where $F_n$ denotes a [[Fibonacci numbers|Fibonacci number]] and $\phi$ denotes the [[golden ratio]]. * {{PaperReference|On a General Fibonacci Identity|1965|John H. Halton|prev=Fibonacci numbers|next=F(-n)=(-1)^(n+1)F(n)}}
  551 bytes (78 words) - 22:32, 25 May 2017
• Sum of odd indexed Fibonacci numbers
  where $F_{2k+1}$ denotes the $2k+1$st [[Fibonacci numbers|Fibonacci number]].
  240 bytes (30 words) - 00:29, 24 May 2017
• Sum of even indexed Fibonacci numbers
  where $F_{2k}$ denotes the $2k$th [[Fibonacci numbers|Fibonacci number]].
  236 bytes (31 words) - 00:30, 24 May 2017
• Sum of squares of Fibonacci numbers
  where $F_k$ denotes the $k$th [[Fibonacci numbers|Fibonacci number]]. * {{PaperReference|A Primer on the Fibonacci Sequence Part I|1963|S.L. Basin|author2=V.E. Hoggatt, Jr.|prev=F(n+m+1)=F(n
  401 bytes (69 words) - 00:35, 25 May 2017
• Catalan's identity
  where $F(n)$ denotes the $n$th [[Fibonacci numbers|Fibonacci number]].
  277 bytes (39 words) - 00:52, 25 May 2017
• Sum of Lucas numbers
  where $L(k)$ denotes the $k$th [[Lucas numbers|Lucas number]]. ...acci Sequence Part I|1963|S.L. Basin|author2=V.E. Hoggatt, Jr.|prev=Sum of Fibonacci numbers|next=F(n+1)F(n-1)-F(n)^2=(-1)^n}}
  389 bytes (62 words) - 00:19, 25 May 2017
• F(n+1)F(n-1)-F(n)^2=(-1)^n
  where $F(n)$ denotes a [[Fibonacci number]]. * {{PaperReference|A Primer on the Fibonacci Sequence Part I|1963|S.L. Basin|author2=V.E. Hoggatt, Jr.|prev=Sum of Lucas
  357 bytes (57 words) - 00:21, 25 May 2017
• L(n+1)L(n-1)-L(n)^2=5(-1)^(n+1)
  where $L(n)$ denotes a [[Lucas numbers|Lucas number]]. * {{PaperReference|A Primer on the Fibonacci Sequence Part I|1963|S.L. Basin|author2=V.E. Hoggatt, Jr.|prev=F(n+1)F(n-1)
  365 bytes (61 words) - 00:25, 25 May 2017
• L(n)=F(n+1)+F(n-1)
  ...numbers|Lucas number]] and $F(n)$ denotes a [[Fibonacci numbers|Fibonacci number]]. * {{PaperReference|A Primer on the Fibonacci Sequence Part I|1963|S.L. Basin|author2=V.E. Hoggatt, Jr.|prev=L(n+1)L(n-1)
  422 bytes (68 words) - 00:28, 25 May 2017
• F(2n+1)=F(n+1)^2+F(n)^2
  where $F(n)$ denotes a [[Fibonacci numbers|Fibonacci number]]. * {{PaperReference|A Primer on the Fibonacci Sequence Part I|1963|S.L. Basin|author2=V.E. Hoggatt, Jr.|prev=L(n)=F(n+1)+
  362 bytes (57 words) - 00:29, 25 May 2017
• F(2n)=F(n+1)^2-F(n-1)^2
  where $F(n)$ denotes a [[Fibonacci numbers|Fibonacci number]]. * {{PaperReference|A Primer on the Fibonacci Sequence Part I|1963|S.L. Basin|author2=V.E. Hoggatt, Jr.|prev=F(2n+1)=F(n+
  358 bytes (57 words) - 00:30, 25 May 2017
• F(2n)=F(n)L(n)
  ...acci numbers|Fibonacci number]] and $L(n)$ denotes a [[Lucas numbers|Lucas number]]. * {{PaperReference|A Primer on the Fibonacci Sequence Part I|1963|S.L. Basin|author2=V.E. Hoggatt, Jr.|prev=F(2n)=F(n+1)
  417 bytes (71 words) - 00:32, 25 May 2017

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