Definition:f

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The LaTeX DLMF and DRMF macro \f represents Function.

This macro is in the category of polynomials.

In math mode, this macro can be called in the following ways:

\f{f} produces Failed to parse (unknown function "\f"): {\displaystyle {\displaystyle \f{f}}}
\f{f}@{x} produces Failed to parse (unknown function "\f"): {\displaystyle {\displaystyle \f{f}@{x}}}

These are defined by

Failed to parse (unknown function "\GenGegenbauer"): {\displaystyle \GenGegenbauer{\alpha}{\beta}{2m}@{x}:={\rm const}\times \Jacobi{\alpha}{\beta}{m}@{2x^2-1}, }

Failed to parse (unknown function "\GenGegenbauer"): {\displaystyle \GenGegenbauer{\alpha}{\beta}{2m+1}@{x}:={\rm const}\times x\,\Jacobi{\alpha}{\beta+1}{m}@{2x^2-1}. }

Then for , we have the orthogonality relation

Failed to parse (unknown function "\GenGegenbauer"): {\displaystyle \int_{-1}^1 \GenGegenbauer{\alpha}{\beta}{m}@{x}\,\GenGegenbauer{\alpha}{\beta}{n}@{x}\,|x|^{2\beta+1} (1-x^2)^\alpha\,dx=0, }

for .

Symbols List

 : function : http://drmf.wmflabs.org/wiki/Definition:f
 : Generalized Gegenbauer polynomial : http://drmf.wmflabs.org/wiki/Definition:GenGegenbauer
 : Jacobi polynomial : http://dlmf.nist.gov/18.3#T1.t1.r3
 : integral : http://dlmf.nist.gov/1.4#iv