Math calculators
Special Function Calculators
13 tools
Gamma, erf, Bessel J/Y/I/K, Lambert W, Beta, and sinc. Not a special-function encyclopedia. Tools may appear in more than one topic.
Popular in Special Functions
Featured tools from the Family registry.
- Special Functions Calculator Real erf, erfc, Gamma, log-gamma, Bessel J_n, Y_n, I_n, and K_n, Lambert W_0 and W_{-1}, Euler beta, incomplete beta, unnormalized sinc, and normalized sinc. Discovery /error-function, /gamma-function, /bessel-function, /bessel-y, /bessel-i, /bessel-k, /lambert-w, /lambert-w-minus-1, /beta-function, /incomplete-beta, /sinc-function, /normalized-sinc. Not factorial. Not CAS. Runs locally.
- Error Function Calculator erf(x) = (2/√π) ∫₀ˣ e^{−t²} dt. Same engine as Special Functions. Odd, erf(0)=0, erf(∞)→1. Not CAS. Runs locally.
- Gamma Function Calculator Γ(x) = ∫₀^∞ t^{x−1} e^{−t} dt except poles at 0, −1, −2, …. Same engine as Special Functions. Not factorial. Not CAS. Runs locally.
- Bessel J Calculator J_n(x) for integer n=0…8. Same engine as Special Functions. Not W_{-1}. Not CAS. Runs locally.
- Lambert W Calculator Principal real W_0(x) for x ≥ −1/e. Same engine as Special Functions. Not incomplete beta. Not CAS. Runs locally.
All Special Functions
Every live calculator in this family. URLs stay /calc/math/…
- Bessel I Calculator I_n(x) for integer n=0…8. Same engine as Special Functions. Not W_{-1}. Not CAS. Runs locally.
- Bessel J Calculator J_n(x) for integer n=0…8. Same engine as Special Functions. Not W_{-1}. Not CAS. Runs locally.
- Bessel K Calculator K_n(x) for integer n=0…8 and x>0. Same engine as Special Functions. Not W_{-1}. Not CAS. Runs locally.
- Bessel Y Calculator Y_n(x) for integer n=0…8 and x>0. Same engine as Special Functions. Not W_{-1}. Not CAS. Runs locally.
- Beta Function Calculator Complete Euler B(x, y) = Γ(x)Γ(y)/Γ(x+y) for x>0, y>0. Same engine as Special Functions. Not incomplete beta. Not CAS. Runs locally.
- Error Function Calculator erf(x) = (2/√π) ∫₀ˣ e^{−t²} dt. Same engine as Special Functions. Odd, erf(0)=0, erf(∞)→1. Not CAS. Runs locally.
- Gamma Function Calculator Γ(x) = ∫₀^∞ t^{x−1} e^{−t} dt except poles at 0, −1, −2, …. Same engine as Special Functions. Not factorial. Not CAS. Runs locally.
- Incomplete Beta Calculator Incomplete beta B_x(a, b) = ∫₀ˣ t^{a−1}(1−t)^{b−1} dt for a>0, b>0, 0≤x≤1. Same engine as Special Functions. Not normalized sinc. Not CAS. Runs locally.
- Lambert W Calculator Principal real W_0(x) for x ≥ −1/e. Same engine as Special Functions. Not incomplete beta. Not CAS. Runs locally.
- Lambert W₋₁ Calculator Real W_{-1}(x) for −1/e ≤ x < 0. Same engine as Special Functions. Not incomplete beta. Not CAS. Runs locally.
- Normalized Sinc Calculator Normalized sinc(x)=sin(πx)/(πx) with sinc(0)=1. Same engine as Special Functions. DSP / numpy convention. Not CAS. Runs locally.
- Sinc Function Calculator Unnormalized sinc(x)=sin(x)/x with sinc(0)=1. Same engine as Special Functions. Not normalized sinc. Not CAS. Runs locally.
- Special Functions Calculator Real erf, erfc, Gamma, log-gamma, Bessel J_n, Y_n, I_n, and K_n, Lambert W_0 and W_{-1}, Euler beta, incomplete beta, unnormalized sinc, and normalized sinc. Discovery /error-function, /gamma-function, /bessel-function, /bessel-y, /bessel-i, /bessel-k, /lambert-w, /lambert-w-minus-1, /beta-function, /incomplete-beta, /sinc-function, /normalized-sinc. Not factorial. Not CAS. Runs locally.