OurBigBook Wikipedia Bot
Documentation
Special functions
OurBigBook Wikipedia Bot
Mathematics
Fields of mathematics
Combinatorics
toc
wiki
nosplit
articles:
266
Table of contents
266
1. Elementary special functions
link
nosplit
Special functions
14
1.1. Exponentials
link
nosplit
Elementary special functions
1.2. Hyperbolic functions
link
nosplit
Elementary special functions
1.3. Inverse hyperbolic functions
link
nosplit
Elementary special functions
1.4. Logarithms
link
nosplit
Elementary special functions
1.5. Trigonometry
link
nosplit
Elementary special functions
1.6. Dirichlet function
link
nosplit
Elementary special functions
1.7. Double exponential function
link
nosplit
Elementary special functions
1.8. Exponential function
link
nosplit
Elementary special functions
1.9. Gudermannian function
link
nosplit
Elementary special functions
1.10. Kronecker delta
link
nosplit
Elementary special functions
1.11. Logarithm
link
nosplit
Elementary special functions
1.12. Ptolemy's table of chords
link
nosplit
Elementary special functions
1.13. Sigmoid function
link
nosplit
Elementary special functions
1.14. Soboleva modified hyperbolic tangent
link
nosplit
Elementary special functions
2. Elliptic functions
link
nosplit
Special functions
26
2.1. Elliptic curves
link
nosplit
Elliptic functions
2.2. Inverse Jacobi elliptic functions
link
nosplit
Elliptic functions
2.3. Inverse lemniscate functions
link
nosplit
Elliptic functions
2.4. Abel elliptic functions
link
nosplit
Elliptic functions
2.5. Carlson symmetric form
link
nosplit
Elliptic functions
2.6. Complex multiplication
link
nosplit
Elliptic functions
2.7. Dedekind eta function
link
nosplit
Elliptic functions
2.8. Dixon elliptic functions
link
nosplit
Elliptic functions
2.9. Elliptic function
link
nosplit
Elliptic functions
2.10. Elliptic integral
link
nosplit
Elliptic functions
2.11. Equianharmonic
link
nosplit
Elliptic functions
2.12. Fundamenta nova theoriae functionum ellipticarum
link
nosplit
Elliptic functions
2.13. Fundamental pair of periods
link
nosplit
Elliptic functions
2.14. Half-period ratio
link
nosplit
Elliptic functions
2.15. J-invariant
link
nosplit
Elliptic functions
2.16. Jacobi theta functions (notational variations)
link
nosplit
Elliptic functions
2.17. Landen's transformation
link
nosplit
Elliptic functions
2.18. Legendre's relation
link
nosplit
Elliptic functions
2.19. Lemniscate elliptic functions
link
nosplit
Elliptic functions
2.20. Modular lambda function
link
nosplit
Elliptic functions
2.21. Nome (mathematics)
link
nosplit
Elliptic functions
2.22. Picard–Fuchs equation
link
nosplit
Elliptic functions
2.23. Quarter period
link
nosplit
Elliptic functions
2.24. Theta function
link
nosplit
Elliptic functions
2.25. Weierstrass elliptic function
link
nosplit
Elliptic functions
2.26. Weierstrass functions
link
nosplit
Elliptic functions
3. Hypergeometric functions
link
nosplit
Special functions
17
3.1. Appell series
link
nosplit
Hypergeometric functions
3.2. Bilateral hypergeometric series
link
nosplit
Hypergeometric functions
3.3. Dougall's formula
link
nosplit
Hypergeometric functions
3.4. Elliptic hypergeometric series
link
nosplit
Hypergeometric functions
3.5. Frobenius solution to the hypergeometric equation
link
nosplit
Hypergeometric functions
3.6. General hypergeometric function
link
nosplit
Hypergeometric functions
3.7. Horn function
link
nosplit
Hypergeometric functions
3.8. Humbert series
link
nosplit
Hypergeometric functions
3.9. Hypergeometric function of a matrix argument
link
nosplit
Hypergeometric functions
3.10. Kampé de Fériet function
link
nosplit
Hypergeometric functions
3.11. Lauricella hypergeometric series
link
nosplit
Hypergeometric functions
3.12. Legendre function
link
nosplit
Hypergeometric functions
3.13. List of hypergeometric identities
link
nosplit
Hypergeometric functions
3.14. MacRobert E function
link
nosplit
Hypergeometric functions
3.15. Meijer G-function
link
nosplit
Hypergeometric functions
3.16. Riemann's differential equation
link
nosplit
Hypergeometric functions
3.17. Schwarz's list
link
nosplit
Hypergeometric functions
4. Special hypergeometric functions
link
nosplit
Special functions
15
4.1. Bessel function
link
nosplit
Special hypergeometric functions
4.2. Bessel–Clifford function
link
nosplit
Special hypergeometric functions
4.3. Coulomb wave function
link
nosplit
Special hypergeometric functions
4.4. Cunningham function
link
nosplit
Special hypergeometric functions
4.5. Error function
link
nosplit
Special hypergeometric functions
4.6. Incomplete Bessel functions
link
nosplit
Special hypergeometric functions
4.7. Kelvin functions
link
nosplit
Special hypergeometric functions
4.8. Lentz's algorithm
link
nosplit
Special hypergeometric functions
4.9. Logarithmic integral function
link
nosplit
Special hypergeometric functions
4.10. Solid harmonics
link
nosplit
Special hypergeometric functions
4.11. Sonine formula
link
nosplit
Special hypergeometric functions
4.12. Spherical harmonics
link
nosplit
Special hypergeometric functions
4.13. Table of spherical harmonics
link
nosplit
Special hypergeometric functions
4.14. Toronto function
link
nosplit
Special hypergeometric functions
4.15. Zonal spherical harmonics
link
nosplit
Special hypergeometric functions
5. Theta functions
link
nosplit
Special functions
6
5.1. Jacobi form
link
nosplit
Theta functions
5.2. Metaplectic group
link
nosplit
Theta functions
5.3. Schottky problem
link
nosplit
Theta functions
5.4. Theta characteristic
link
nosplit
Theta functions
5.5. Theta divisor
link
nosplit
Theta functions
5.6. Theta function of a lattice
link
nosplit
Theta functions
6. Zeta and L-functions
link
nosplit
Special functions
87
6.1. Airy zeta function
link
nosplit
Zeta and L-functions
6.2. Apéry's theorem
link
nosplit
Zeta and L-functions
6.3. Arakawa–Kaneko zeta function
link
nosplit
Zeta and L-functions
6.4. Arithmetic zeta function
link
nosplit
Zeta and L-functions
6.5. Artin L-function
link
nosplit
Zeta and L-functions
6.6. Artin conductor
link
nosplit
Zeta and L-functions
6.7. Artin–Mazur zeta function
link
nosplit
Zeta and L-functions
6.8. Automorphic L-function
link
nosplit
Zeta and L-functions
6.9. Barnes zeta function
link
nosplit
Zeta and L-functions
6.10. Basel problem
link
nosplit
Zeta and L-functions
6.11. Beurling zeta function
link
nosplit
Zeta and L-functions
6.12. Birch and Swinnerton-Dyer conjecture
link
nosplit
Zeta and L-functions
6.13. Brumer–Stark conjecture
link
nosplit
Zeta and L-functions
6.14. Chowla–Mordell theorem
link
nosplit
Zeta and L-functions
6.15. Clausen function
link
nosplit
Zeta and L-functions
6.16. Dedekind zeta function
link
nosplit
Zeta and L-functions
6.17. Dirichlet's theorem on arithmetic progressions
link
nosplit
Zeta and L-functions
6.18. Dirichlet L-function
link
nosplit
Zeta and L-functions
6.19. Dirichlet beta function
link
nosplit
Zeta and L-functions
6.20. Dirichlet character
link
nosplit
Zeta and L-functions
6.21. Dirichlet eta function
link
nosplit
Zeta and L-functions
6.22. Divisor function
link
nosplit
Zeta and L-functions
6.23. Dwork conjecture
link
nosplit
Zeta and L-functions
6.24. Eichler–Shimura congruence relation
link
nosplit
Zeta and L-functions
6.25. Equivariant L-function
link
nosplit
Zeta and L-functions
6.26. Euler product
link
nosplit
Zeta and L-functions
6.27. Explicit formulae for L-functions
link
nosplit
Zeta and L-functions
6.28. Feller–Tornier constant
link
nosplit
Zeta and L-functions
6.29. Functional equation (L-function)
link
nosplit
Zeta and L-functions
6.30. Gan–Gross–Prasad conjecture
link
nosplit
Zeta and L-functions
6.31. Generalized Riemann hypothesis
link
nosplit
Zeta and L-functions
6.32. Goss zeta function
link
nosplit
Zeta and L-functions
6.33. Grand Riemann hypothesis
link
nosplit
Zeta and L-functions
6.34. Hadjicostas's formula
link
nosplit
Zeta and L-functions
6.35. Hardy–Littlewood zeta-function conjectures
link
nosplit
Zeta and L-functions
6.36. Hasse–Weil zeta function
link
nosplit
Zeta and L-functions
6.37. Hecke character
link
nosplit
Zeta and L-functions
6.38. Hideo Shimizu
link
nosplit
Zeta and L-functions
6.39. Hilbert–Pólya conjecture
link
nosplit
Zeta and L-functions
6.40. Hurwitz zeta function
link
nosplit
Zeta and L-functions
6.41. Igusa zeta function
link
nosplit
Zeta and L-functions
6.42. L-function
link
nosplit
Zeta and L-functions
6.43. Langlands program
link
nosplit
Zeta and L-functions
6.44. Langlands–Deligne local constant
link
nosplit
Zeta and L-functions
6.45. Lefschetz zeta function
link
nosplit
Zeta and L-functions
6.46. Lerch zeta function
link
nosplit
Zeta and L-functions
6.47. Li's criterion
link
nosplit
Zeta and L-functions
6.48. Lindelöf hypothesis
link
nosplit
Zeta and L-functions
6.49. List of zeta functions
link
nosplit
Zeta and L-functions
6.50. Local Langlands conjectures
link
nosplit
Zeta and L-functions
6.51. Local zeta function
link
nosplit
Zeta and L-functions
6.52. Matsumoto zeta function
link
nosplit
Zeta and L-functions
6.53. Montgomery's pair correlation conjecture
link
nosplit
Zeta and L-functions
6.54. Motivic L-function
link
nosplit
Zeta and L-functions
6.55. Multiple zeta function
link
nosplit
Zeta and L-functions
6.56. P-adic L-function
link
nosplit
Zeta and L-functions
6.57. Prime zeta function
link
nosplit
Zeta and L-functions
6.58. Proof of the Euler product formula for the Riemann zeta function
link
nosplit
Zeta and L-functions
6.59. Ramanujan tau function
link
nosplit
Zeta and L-functions
6.60. Ramanujan–Petersson conjecture
link
nosplit
Zeta and L-functions
6.61. Rankin–Selberg method
link
nosplit
Zeta and L-functions
6.62. Riemann Xi function
link
nosplit
Zeta and L-functions
6.63. Riemann hypothesis
link
nosplit
Zeta and L-functions
6.64. Riemann zeta function
link
nosplit
Zeta and L-functions
6.65. Riemann–Siegel formula
link
nosplit
Zeta and L-functions
6.66. Riemann–Siegel theta function
link
nosplit
Zeta and L-functions
6.67. Riesz function
link
nosplit
Zeta and L-functions
6.68. Ruelle zeta function
link
nosplit
Zeta and L-functions
6.69. Selberg's zeta function conjecture
link
nosplit
Zeta and L-functions
6.70. Selberg class
link
nosplit
Zeta and L-functions
6.71. Shimizu L-function
link
nosplit
Zeta and L-functions
6.72. Shimura variety
link
nosplit
Zeta and L-functions
6.73. Shintani zeta function
link
nosplit
Zeta and L-functions
6.74. Siegel zero
link
nosplit
Zeta and L-functions
6.75. Special values of L-functions
link
nosplit
Zeta and L-functions
6.76. Standard L-function
link
nosplit
Zeta and L-functions
6.77. Stieltjes constants
link
nosplit
Zeta and L-functions
6.78. Subgroup growth
link
nosplit
Zeta and L-functions
6.79. Tate's thesis
link
nosplit
Zeta and L-functions
6.80. Turing's method
link
nosplit
Zeta and L-functions
6.81. Waldspurger's theorem
link
nosplit
Zeta and L-functions
6.82. Weil's criterion
link
nosplit
Zeta and L-functions
6.83. Weil conjectures
link
nosplit
Zeta and L-functions
6.84. Z function
link
nosplit
Zeta and L-functions
6.85. ZetaGrid
link
nosplit
Zeta and L-functions
6.86. Zeta function (operator)
link
nosplit
Zeta and L-functions
6.87. Zeta function universality
link
nosplit
Zeta and L-functions
7. Airy function
link
nosplit
Special functions
8. Anger function
link
nosplit
Special functions
9. Baer function
link
nosplit
Special functions
10. Barnes integral
link
nosplit
Special functions
11. Bateman Manuscript Project
link
nosplit
Special functions
12. Bateman function
link
nosplit
Special functions
13. Bickley–Naylor functions
link
nosplit
Special functions
14. Bounded type (mathematics)
link
nosplit
Special functions
15. Boxcar function
link
nosplit
Special functions
16. Buchstab function
link
nosplit
Special functions
17. Böhmer integral
link
nosplit
Special functions
18. Cantor function
link
nosplit
Special functions
19. Carotid–Kundalini function
link
nosplit
Special functions
20. Chandrasekhar's H-function
link
nosplit
Special functions
21. Chandrasekhar's X- and Y-function
link
nosplit
Special functions
22. Chapman function
link
nosplit
Special functions
23. Clausen's formula
link
nosplit
Special functions
24. Complete Fermi–Dirac integral
link
nosplit
Special functions
25. Confluent hypergeometric function
link
nosplit
Special functions
26. Conical function
link
nosplit
Special functions
27. Coshc function
link
nosplit
Special functions
28. Crenel function
link
nosplit
Special functions
29. Dawson function
link
nosplit
Special functions
30. Debye function
link
nosplit
Special functions
31. Dickman function
link
nosplit
Special functions
32. Einstein function
link
nosplit
Special functions
33. Entire function
link
nosplit
Special functions
34. Exponential integral
link
nosplit
Special functions
35. Ferrers function
link
nosplit
Special functions
36. Fox H-function
link
nosplit
Special functions
37. Fresnel integral
link
nosplit
Special functions
38. Goodwin–Staton integral
link
nosplit
Special functions
39. Griewank function
link
nosplit
Special functions
40. Hankel contour
link
nosplit
Special functions
41. Harish-Chandra's Ξ function
link
nosplit
Special functions
42. Heaviside step function
link
nosplit
Special functions
43. Herglotz–Zagier function
link
nosplit
Special functions
44. Heun function
link
nosplit
Special functions
45. Holonomic function
link
nosplit
Special functions
46. Hough function
link
nosplit
Special functions
47. Hyperbolastic functions
link
nosplit
Special functions
48. Incomplete Bessel K function/generalized incomplete gamma function
link
nosplit
Special functions
49. Incomplete Fermi–Dirac integral
link
nosplit
Special functions
50. Incomplete polylogarithm
link
nosplit
Special functions
51. Inverse tangent integral
link
nosplit
Special functions
52. Jacobi elliptic functions
link
nosplit
Special functions
53. Jacobi zeta function
link
nosplit
Special functions
54. Kontorovich–Lebedev transform
link
nosplit
Special functions
55. Kummer's function
link
nosplit
Special functions
56. Lambert W function
link
nosplit
Special functions
57. Lamé function
link
nosplit
Special functions
58. Legendre chi function
link
nosplit
Special functions
59. Legendre form
link
nosplit
Special functions
60. List of eponyms of special functions
link
nosplit
Special functions
61. Logit
link
nosplit
Special functions
62. Lommel function
link
nosplit
Special functions
63. Mathieu function
link
nosplit
Special functions
64. Mayer f-function
link
nosplit
Special functions
65. Minkowski's question-mark function
link
nosplit
Special functions
66. Mittag-Leffler function
link
nosplit
Special functions
67. Modular form
link
nosplit
Special functions
68. Neville theta functions
link
nosplit
Special functions
69. Oblate spheroidal wave function
link
nosplit
Special functions
70. Painlevé transcendents
link
nosplit
Special functions
71. Parabolic cylinder function
link
nosplit
Special functions
72. Pochhammer contour
link
nosplit
Special functions
73. Prolate spheroidal wave function
link
nosplit
Special functions
74. Q-function
link
nosplit
Special functions
75. Ramp function
link
nosplit
Special functions
76. Real analytic Eisenstein series
link
nosplit
Special functions
77. Rectangular function
link
nosplit
Special functions
78. Ruler function
link
nosplit
Special functions
79. Scorer's function
link
nosplit
Special functions
80. Selberg integral
link
nosplit
Special functions
81. Sinhc function
link
nosplit
Special functions
82. Spence's function
link
nosplit
Special functions
83. Spin-weighted spherical harmonics
link
nosplit
Special functions
84. Step function
link
nosplit
Special functions
85. Struve function
link
nosplit
Special functions
86. Strömgren integral
link
nosplit
Special functions
87. Student's t-distribution
link
nosplit
Special functions
88. Synchrotron function
link
nosplit
Special functions
89. Tak (function)
link
nosplit
Special functions
90. Tanc function
link
nosplit
Special functions
91. Tanhc function
link
nosplit
Special functions
92. Thomae's function
link
nosplit
Special functions
93. Tracy–Widom distribution
link
nosplit
Special functions
94. Transcendental function
link
nosplit
Special functions
95. Transport function
link
nosplit
Special functions
96. Triangular function
link
nosplit
Special functions
97. Trigonometric integral
link
nosplit
Special functions
98. Voigt profile
link
nosplit
Special functions
99. Walsh function
link
nosplit
Special functions
100. Whipple formulae
link
nosplit
Special functions
101. Wright omega function
link
nosplit
Special functions
Ancestors
Combinatorics
Fields of mathematics
Mathematics
OurBigBook Wikipedia Bot