Latest revision as of 13:31, 8 November 2024

Special functions are ubiquitous in mathematics and applications of mathematics. The term applies to such a wide range of functions that no single source contains all of them. We aim to remedy this problem.

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 Special functions are ubiquitous in mathematics and applications of mathematics. The term applies to such a wide range of functions that no single source contains all of them. We aim to remedy this problem.
+<b><u>Registration</u></b>
+Due to a resurgence of automated spam bots, account registration and anonymous editing is currently disabled. Please contact Tom Cuchta (tomcuchta@gmail.com) to gain access to edit the wiki.
 =Special functions=
@@ Line 35: / Line 38: @@
 </div>
+[[Bickley-Naylor]]<br />
 [[Carlitz-Goss Gamma function]]<br />
 [[Clausen cosine]]<br />
@@ Line 53: / Line 57: @@
 [[Maass forms]] <br />
 [[Meijer G-function]]<br />
+[[Mittag-Leffler]]<br />
 [[Modular form]]<br />
 [[Mock modular forms]]<br />
@@ Line 233: / Line 238: @@
 [[Böhmer C]]<br />
 [[Böhmer S]]<br />
+[[Entire exponential integral]]<br />
 ==Jacobi theta functions==
@@ Line 254: / Line 260: @@
 [[Matrix cosine]]<br />
 [[Trace]]<br />
+===Matrix hypergeometric functions===
+[[Matrix hypergeometric pFq]]<br />
+[[Matrix hypergeometric 0F3]]<br />
+[[Matrix hypergeometric 1F1]]<br />
+[[Matrix hypergeometric 1F2]]<br />
+[[Matrix hypergeometric 2F0]]<br />
+[[Matrix hypergeometric 2F3]]<br />
+[[Matrix hypergeometric 3F2]]<br />
+[[Matrix hypergeometric 4F1]]<br />
 ==Operators==
@@ Line 274: / Line 290: @@
 ==Probability distributions==
 ===Continuous distributions===
-[[Arcsin distribution]]<br />
+====Probability density funcitons====
-[[Beta distribution]]<br />
+[[Arcsin pdf]]<br />
-[[Cauchy distribution]]<br />
+[[Beta pdf]]<br />
-[[Chi-squared distribution]]<br />
+[[Cauchy pdf]]<br />
-[[Exponential distribution]]<br />
+[[Chi-squared pdf]]<br />
-[[F distribution]]<br />
+[[Exponential pdf]]<br />
-[[Gamma distribution]]<br />
+[[F pdf]]<br />
-[[Laplace distribution]]<br />
+[[Gamma pdf]]<br />
-[[Log-normal distribution]]<br />
+[[Laplace pdf]]<br />
-[[Normal distribution]]<br />
+[[Log-normal pdf]]<br />
-[[Pareto distribution]]<br />
+[[Normal pdf]]<br />
-[[Student's t distribution]]<br />
+[[Pareto pdf]]<br />
-[[Uniform distribution]]<br />
+[[Student's t pdf]]<br />
-[[Weibull distribution]]<br />
+[[Continuous uniform pdf]]<br />
+[[Weibull pdf]]<br />
+====Cumulative Density Functions====
+[[Arcsin cdf]]<br />
+[[Beta cdf]]<br />
+[[Cauchy cdf]]<br />
+[[Chi-squared cdf]]<br />
+[[Exponential cdf]]<br />
+[[F cdf]]<br />
+[[Gamma cdf]]<br />
+[[Laplace cdf]]<br />
+[[Log-normal cdf]]<br />
+[[Normal cdf]]<br />
+[[Pareto cdf]]<br />
+[[Student's t cdf]]<br />
+[[Continuous uniform cdf]]<br />
+[[Weibull cdf]]<br />
 ===Discrete distributions===
@@ Line 308: / Line 341: @@
 [[Cyclotomic polynomials]]<br />
 [[Denisyuk polynomials]]<br />
+[[Eberlein polynomials]]<br />
 [[Hahn polynomial]]<br />
 [[Humbert polynomials]]<br />
@@ Line 368: / Line 402: @@
 [[q-Gaussian distribution | $q$-Gaussian distribution]]<br />
 [[q-Hermite polynomial | $q$-Hermite polynomial]]<br />
+[[q-Hurwitz zeta|$q$-Hurwitz zeta]]<br />
 [[q-Pochhammer | $q$-Pochhammer symbol]]<br />
 [[q-Pollaczek polynomial]]<br />
@@ Line 376: / Line 411: @@
 [[q-Theta function | $q$-Theta function]]<br />
 [[q-ultraspherical polynomial|$q$-ultraspherical polynomial]]<br />
+[[q-zeta|$q$-zeta]]<br />
 [[Second q-shifted factorial|Second $q$-shifted factorial]]<br />
 [[Tsallis q-exponential|Tsallis $q$-exponential]]<br />
@@ Line 404: / Line 440: @@
 [[Genocchi numbers]]<br />
 [[Harmonic number]]<br />
+[[Idoneal number]]<br />
+[[Jacobsthal numbers]]<br />
 [[Signed Lah numbers]]<br />
 [[Unsigned Lah numbers]]<br />
@@ Line 491: / Line 529: @@
 [[Multiple zeta function]]<br />
 [[p-adic zeta function | $p$-adic zeta function]]<br />
+[[q-Hurwitz zeta|$q$-Hurwitz zeta]]<br />
+[[q-zeta|$q$-zeta]]<br />
 [[Reciprocal zeta function]]<br />
 [[Ruelle zeta function]]<br />
@@ Line 510: / Line 550: @@
 =Special constants=
+[[Algebraic]] <br />
+[[Transcendental]]
 {| class="wikitable sortable"
 |-
@@ Line 627: / Line 669: @@
 |-
 | [[Thue constant]] || || $0.8590997969\ldots$
+|-
+| [[Trott's constant]] || || $0.10841015\ldots$
 |-
 | [[Twin prime constant]] || ||
@@ Line 692: / Line 736: @@
 =External Links=
 [http://authors.library.caltech.edu/43491/ Higher transcendental functions (Bateman project)]<br />
-[http://dualaud.net/txt/rainvillespecialfunctions.php Solution manual to Rainville's "Special Functions"]<br />
+[https://github.com/tomcuchta/rainvillesfsolutions Solution manual to Rainville's "Special Functions"]<br />
 [http://web.mst.edu/~lmhall/SPFNS/spfns.pdf "Special Functions" by Leon Hall]<br />
 [http://www.johndcook.com/special_function_diagram.html Relations between special functions by John D. Cook]<br />

Name	Notation	Value
Apéry's constant	$\zeta(3)$	$1.2020569031595942854 \ldots$
Artin constant	$C_{\mathrm{Artin}}$	$0.3739558136\ldots$
Brun's constant	$B_2$	$1.9021605831\ldots$
Cahen's constant	$C$	$0.64341054629\ldots$
Catalan constant	$G$	$0.915965594177219015054603514932384110774 \ldots$
Chaitin's constant
Champernowne constant	$C_{10}$	$0.12345678910111213141516171819202122232425\ldots$
Conway's constant		$1.303577269034 \ldots$
Copeland-Erdős constant		$0.23571113171923...$
Euler's number	$e$	$2.71828182846 \ldots$
Erdős-Borwein Constant	$E$	$1.606695152415291763\ldots$
Euler-Mascheroni constant	$\gamma$	$0.5772156649015328606065120900824024310421593359399235\ldots$
Feigenbaum constants		$4.669201609102990671853203820466201617258185577475768632745651 \ldots$
Freiman constant	$F$	$4.5278295661\ldots$
Fransén–Robinson constant		$2.807770242028519365221501186557772932308085920930198291220054 \ldots$
Gauss' constant	$G$	$0.83462684167\ldots$
Gieseking constant	$G$	$1.01494160640965\ldots$
Gelfond constant	$e^{\pi}$	$23.14069263277926900572908636794854738026610624260021199344504 \ldots$
Gelfond–Schneider constant	$2^{\sqrt{2}}$	$2.665144142690225188650297249873139848274211313714659492835979 \ldots$
Glaisher–Kinkelin constant	$A$	$1.2824271291 \ldots$
Goh-Schmutz constant	$C$	$1.1178641511899\ldots$
Golden ratio	$\phi$	$1.618033988749894848204586834365638117720309179805762862135448 \ldots$
Gompertz constant	$G$	$0.596347362323\ldots$
Graham's number
Hall-Montgomery constant	$\delta_0$	$0.17150049\ldots$
Imaginary number	$i$	$\sqrt{-1}$
Jenny's constants	$J$	$867.5309\ldots$
Kaprekar's constant		$6174$
Khinchin's constant	$K$	$2.685452001065306445309714835481795693820382293994462953051152 \ldots$
Komornik–Loreti constant	$q$	$1.787231650\ldots$
Legendre's constant	$B$	$1$
Lefschetz number
Lévy's constant
Liouville constant
Meissel-Mertens constant	$M$	$0.26149721284764278375...$
Mills' constant	$M$	$1.306377883863080690468614492602605712916784585156713644368053 \ldots$
Nested radical constant	$C$	$1.75793275\ldots$
Norton's constant	$B$	$0.06535142\ldots$
Omega constant	$\Omega$	$0.5671432904097838729\ldots$
Paper folding constant	$P$	$0.85073618820186\ldots$
Pell constant	$P$	$0.58057755820489\ldots$
Pi	$\pi$	$3.141592653589793238462643383279502884197169399375105820974944 \ldots$
Porter's constant	$C$	$1.4670780794\ldots$
q-pi	$\pi_q$
Rabbit constant	$R$	$0.7098034428612913146\ldots$
Ramanujan constant	$R$	$262537412640768743.9999999999992500\ldots$
Reciprocal Fibonacci constant	$\psi$	$3.35988566624317755\ldots$
Rutherford constant	$K_R$	$0.8227\ldots$
Shallit Constant
Sierpiński constant	$S$	$0.8228252496\ldots$
Silver ratio	$\delta_s$	$2.4142135623730950488 \ldots$
Soldner's Constant	$\mu$	$1.45136923488338105028396848589202744949\ldots$
Square root spiral constant		$-2.1577829966\ldots$
Stieltjes constants	$\gamma_n$
Ternary Champernowne constant	$C_3$	$0.598958167538433\ldots$
Theodorus constant		$1.8600250792\ldots$
Thue constant		$0.8590997969\ldots$
Trott's constant		$0.10841015\ldots$
Twin prime constant
White House switchboard constants	$W$	$0.2024561414 \ldots$
Wyler constant	$\alpha_W$
Zolotarev-Schur constant

Difference between revisions of "Main Page"

Latest revision as of 13:31, 8 November 2024

Contents

Special functions

Bessel functions and friends

*-c functions

Continuous nowhere-differentiable functions and friends

Defined by a differential equation

Elliptic functions

Error function and friends

Figurate numbers

Gamma function and friends

Hypergeometric series

*-integral functions

Jacobi theta functions

Logarithm function and friends

Matrix functions

Matrix hypergeometric functions

Operators

Polynomials

Probability distributions

Continuous distributions

Probability density funcitons

Cumulative Density Functions

Discrete distributions

$q$-calculus

$q$-special functions

Special functions in number theory

Special sequences

Trigonometric functions

Depreciated trigonometric functions

Zeta functions

Arithmetic Operations

Special constants

Numbers

Tools from calculus

Other

External Links

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