# Main Page

The **NIST Digital Repository of Mathematical Formulae** is designed for
a mathematically literate audience and should

- facilitate interaction among a community of mathematicians and scientists interested in compendia formulae data for
**orthogonal polynomials and special functions**; - be expandable, allowing the input of new formulae from the literature;
- represent the context-free full semantic information concerning individual formulas;
- have a user friendly, consistent, and hyperlinkable viewpoint and authoring perspective;
- contain easily searchable mathematics; and
- take advantage of modern MathML tools for easy to read, scalably rendered content driven mathematics.

For more information see Digital Repository of Mathematical Formulae or arXiv:1404.6519.

## Contents

## Sample Seeding Project Implementations

`DLMF`: Zeta and Related Functions

`KLS` and `KLSadd`: Orthogonal Polynomials

## Useful Pages

How to Upload Your Project to GitHub

How to get access to Wikilabs/Wikitech

## Sample formula home pages with DLMF proofs given

- Formula:DLMF:25.2:E9
- Formula:DLMF:25.5:E2
- Formula:DLMF:25.5:E4
- Formula:DLMF:25.5:E6
- Formula:DLMF:25.8:E7
- Formula:DLMF:25.8:E8
- Formula:DLMF:25.11:E7
- Formula:DLMF:25.11:E10
- Formula:DLMF:25.11:E11
- Formula:DLMF:25.11:E15
- Formula:DLMF:25.11:E17
- Formula:DLMF:25.11:E24
- Formula:DLMF:25.11:E27
- Formula:DLMF:25.11:E28
- Formula:DLMF:25.11:E30
- Formula:DLMF:25.11:E31
- Formula:DLMF:25.11:E35

# Digital Repository of Mathematical Formulae

- Algebraic and Analytic Methods
- Asymptotic Approximations
- Numerical Methods
- Elementary Functions
- Gamma Function
- Exponential, Logarithmic, Sine, and Cosine Integrals
- Error Functions, Dawson’s and Fresnel Integrals
- Incomplete Gamma and Related Functions
- Airy and Related Functions
- Bessel Functions
- Struve and Related Functions
- Parabolic Cylinder Functions
- Confluent Hypergeometric Functions
- Legendre and Related Functions
- Hypergeometric Function
- Generalized Hypergeometric Functions and Meijer
*G*-Function *q*-Hypergeometric and Related Functions- Orthogonal Polynomials
- Elliptic Integrals
- Theta Functions
- Multidimensional Theta Functions
- Jacobian Elliptic Functions
- Weierstrass Elliptic and Modular Functions
- Bernoulli and Euler Polynomials
- Zeta and Related Functions
- Combinatorial Analysis
- Functions of Number Theory
- Mathieu Functions and Hill’s Equation
- Lamé Functions
- Spheroidal Wave Functions
- Heun Functions
- Painlevé Transcendents
- Coulomb Functions
*3j,6j,9j*Symbols- Functions of Matrix Argument
- Integrals with Coalescing Saddles

## Definition Pages

- AffqKrawtchouk
- AlSalamCarlitzI
- AlSalamCarlitzII
- AlSalamIsmail
- AntiDer
- BesselPolyIIparam
- BesselPolyTheta
- bigqJacobiIVparam
- bigqLaguerre
- bigqLegendre
- CiglerqChebyT
- CiglerqChebyU
- ctsbigqHermite
- ctsdualqHahn
- ctsqHahn
- ctsqJacobi
- ctsqLaguerre
- ctsqLegendre
- f
- GenHermite
- GottliebLaguerre
- Int
- JacksonqBesselII
- JacksonqBesselIII
- littleqLegendre
- lrselection
- monicAlSalamCarlitzI
- monicAlSalamCarlitzII
- monicAlSalamChihara
- monicAskeyWilson
- monicBesselPoly
- monicbigqJacobi
- monicbigqLaguerre
- monicbigqLegendre
- monicCharlier
- monicChebyT
- monicChebyU
- monicctsbigqHermite
- monicctsdualHahn
- monicctsdualqHahn
- monicctsHahn
- monicctsqHahn
- monicctsqHermite
- monicctsqJacobi
- monicctsqLaguerre
- monicctsqLegendre
- monicctsqUltra
- monicdiscrqHermiteI
- monicdiscrqHermiteII
- monicdualHahn
- monicdualqHahn
- monicdualqKrawtchouk
- monicHahn
- monicHermite
- monicJacobi
- monicKrawtchouk
- monicLaguerre
- monicLegendrePoly
- moniclittleqJacobi
- moniclittleqLaguerre
- moniclittleqLegendre
- monicMeixner
- monicMeixnerPollaczek
- monicpseudoJacobi
- monicqBesselPoly
- monicqCharlier
- monicqKrawtchouk
- monicqLaguerre
- monicqMeixner
- monicqMeixnerPollaczek
- monicqRacah
- monicqtmqKrawtchouk
- monicRacah
- monicStieltjesWigert
- monicUltra
- monicWilson
- NeumannFactor
- normctsdualHahnStilde
- normctsHahnptilde
- normJacobiR
- normWilsonWtilde
- poly
- qBesselPoly
- qCharlier
- qDigamma
- qHyperrWs
- qExpKLS
- qexpKLS
- qcosKLS
- qMeixner
- qKrawtchouk
- monicqHahn
- dualqHahn
- dualqKrawtchouk
- littleqLaguerre
- qsinKLS
- qSinKLS
- qCosKLS
- Wilson
- Racah
- ctsdualHahn
- ctsHahn
- Hahn
- dualHahn
- qRacah
- normctsdualqHahnptilde
- normctsqHahnptilde
- qHahn
- AlSalamChihara
- qinvAlSalamChihara
- monicqinvAlSalamChihara
- monicAffqKrawtchouk
- qMeixnerPollaczek
- qtmqKrawtchouk
- qLaguerre
- ctsqHermite
- StieltjesWigert
- discrqHermiteI
- discrqHermiteII
- StieltjesConstants

# Copyright

Pursuant to U.S. Code, Title 17, Chapter 1, Section 105:

Copyright protection under this title is not available for any work of the United States Government, but the United States Government is not precluded from receiving and holding copyrights transferred to it by assignment, bequest, or otherwise.

the National Institute of Standards and Technology (NIST), United States Department of Commerce, this website, a work of the United States Government, is in the public domain.

# Disclaimer

While NIST has made every effort to ensure the accuracy and reliability of the information in the DLMF, the DLMF is expressly provided “AS-IS.” NIST makes NO WARRANTY OF ANY TYPE, including no warranties of merchantability or fitness for a particular purpose. NIST makes no warranties or representations as to the correctness, accuracy, or reliability of the DLMF. As a condition of using the DLMF, you explicitly release NIST from any and all liabilities for any damage of any type that may result from errors or omissions in the DLMF.

Certain products, commercial and otherwise, are mentioned in the DLMF. These mentions are for informational purposes only, and do not imply recommendation or endorsement by NIST.

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