# Definition:f

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 (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://vmext-demo.wmflabs.org/v1/":): {\displaystyle {\displaystyle \f{f}}}****\f{f}@{x}**produces**Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://vmext-demo.wmflabs.org/v1/":): {\displaystyle {\displaystyle \f{f}@{x}}}**

These are defined by

**Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://vmext-demo.wmflabs.org/v1/":): {\displaystyle \GenGegenbauer{\alpha}{\beta}{2m}@{x}:={\rm const}\times \Jacobi{\alpha}{\beta}{m}@{2x^2-1}, }**

**Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://vmext-demo.wmflabs.org/v1/":): {\displaystyle \GenGegenbauer{\alpha}{\beta}{2m+1}@{x}:={\rm const}\times x\,\Jacobi{\alpha}{\beta+1}{m}@{2x^2-1}. }**

Then for **Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://vmext-demo.wmflabs.org/v1/":): {\displaystyle \alpha,\beta>-1}**
, we have the orthogonality relation

**Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://vmext-demo.wmflabs.org/v1/":): {\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 **Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://vmext-demo.wmflabs.org/v1/":): {\displaystyle m\ne n}**
.

## Symbols List

**Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://vmext-demo.wmflabs.org/v1/":): {\displaystyle {\displaystyle {f}}}**
: function : http://drmf.wmflabs.org/wiki/Definition:f

**Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://vmext-demo.wmflabs.org/v1/":): {\displaystyle {\displaystyle S^{(\alpha,\beta)}_{n}}}**
: Generalized Gegenbauer polynomial : http://drmf.wmflabs.org/wiki/Definition:GenGegenbauer

**Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://vmext-demo.wmflabs.org/v1/":): {\displaystyle {\displaystyle P^{(\alpha,\beta)}_{n}}}**
: Jacobi polynomial : http://dlmf.nist.gov/18.3#T1.t1.r3

**Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://vmext-demo.wmflabs.org/v1/":): {\displaystyle {\displaystyle \int}}**
: integral : http://dlmf.nist.gov/1.4#iv