Keyword : Special functions

S01BAF	$\ln (1 + x)$
S01EAF	Complex exponential, $e^{z}$
S07AAF	$\tan x$
S09AAF	$\arcsin x$
S09ABF	$\arccos x$
S10AAF	$\tanh x$
S10ABF	$\sinh x$
S10ACF	$\cosh x$
S11AAF	$arctanh x$
S11ABF	$arcsinh x$
S11ACF	$arccosh x$
S13AAF	Exponential integral $E_{1} (x)$
S13ACF	Cosine integral $Ci (x)$
S13ADF	Sine integral $Si (x)$
S14AAF	Gamma function
S14ABF	Log gamma function, real argument
S14ACF	$ψ (x) - \ln x$
S14ADF	Scaled derivatives of $ψ (x)$
S14AEF	Polygamma function $ψ^{(n)} (x)$ for real $x$
S14AFF	Polygamma function $ψ^{(n)} (z)$ for complex $z$
S14AGF	Logarithm of the gamma function $\ln Γ (z)$ , complex argument
S14AHF	Scaled log gamma function
S14BAF	Incomplete gamma functions $P (a, x)$ and $Q (a, x)$
S14CBF	Logarithm of the beta function $\ln (B, a, b)$
S14CCF	Incomplete beta function $I_{x} (a, b)$ and its complement $1 - I_{x}$
S15ABF	Cumulative Normal distribution function $P (x)$
S15ACF	Complement of cumulative Normal distribution function $Q (x)$
S15ADF	Complement of error function $erfc (x)$
S15AEF	Error function $\erf (x)$
S15AFF	Dawson's integral
S15AGF	Scaled complement of error function, $erfcx (x)$
S15DDF	Scaled complex complement of error function, $\exp (- z^{2}) erfc (- i z)$
S17ACF	Bessel function $Y_{0} (x)$
S17ADF	Bessel function $Y_{1} (x)$
S17AEF	Bessel function $J_{0} (x)$
S17AFF	Bessel function $J_{1} (x)$
S17AGF	Airy function $Ai (x)$
S17AHF	Airy function $Bi (x)$
S17AJF	Airy function ${Ai}^{'} (x)$
S17AKF	Airy function ${Bi}^{'} (x)$
S17ALF	Zeros of Bessel functions $J_{α} (x)$ , $J_{α}^{'} (x)$ , $Y_{α} (x)$ or $Y_{α}^{'} (x)$
S17AQF	Bessel function vectorized $Y_{0} (x)$
S17ARF	Bessel function vectorized $Y_{1} (x)$
S17ASF	Bessel function vectorized $J_{0} (x)$
S17ATF	Bessel function vectorized $J_{1} (x)$
S17AUF	Airy function vectorized $Ai (x)$
S17AVF	Airy function vectorized $Bi (x)$
S17AWF	Airy function vectorized ${Ai}^{'} (x)$
S17AXF	Airy function vectorized ${Bi}^{'} (x)$
S17DCF	Bessel functions $Y_{ν + a} (z)$ , real $a \geq 0$ , complex $z$ , $ν = 0, 1, 2, \dots$
S17DEF	Bessel functions $J_{ν + a} (z)$ , real $a \geq 0$ , complex $z$ , $ν = 0, 1, 2, \dots$
S17DGF	Airy functions $Ai (z)$ and ${Ai}^{'} (z)$ , complex $z$
S17DHF	Airy functions $Bi (z)$ and ${Bi}^{'} (z)$ , complex $z$
S17DLF	Hankel functions $H_{ν + a}^{(j)} (z)$ , $j = 1, 2$ , real $a \geq 0$ , complex $z$ , $ν = 0, 1, 2, \dots$
S18ACF	Modified Bessel function $K_{0} (x)$
S18ADF	Modified Bessel function $K_{1} (x)$
S18AEF	Modified Bessel function $I_{0} (x)$
S18AFF	Modified Bessel function $I_{1} (x)$
S18AQF	Modified Bessel function vectorized $K_{0} (x)$
S18ARF	Modified Bessel function vectorized $K_{1} (x)$
S18ASF	Modified Bessel function vectorized $I_{0} (x)$
S18ATF	Modified Bessel function vectorized $I_{1} (x)$
S18CCF	Scaled modified Bessel function $e^{x} K_{0} (x)$
S18CDF	Scaled modified Bessel function $e^{x} K_{1} (x)$
S18CEF	Scaled modified Bessel function $e^{- \|x\|} I_{0} (x)$
S18CFF	Scaled modified Bessel function $e^{- \|x\|} I_{1} (x)$
S18CQF	Scaled modified Bessel function vectorized $e^{x} K_{0} (x)$
S18CRF	Scaled modified Bessel function vectorized $e^{x} K_{1} (x)$
S18CSF	Scaled modified Bessel function vectorized $e^{- \|x\|} I_{0} (x)$
S18CTF	Scaled modified Bessel function vectorized $e^{- \|x\|} I_{1} (x)$
S18DCF	Modified Bessel functions $K_{ν + a} (z)$ , real $a \geq 0$ , complex $z$ , $ν = 0, 1, 2, \dots$
S18DEF	Modified Bessel functions $I_{ν + a} (z)$ , real $a \geq 0$ , complex $z$ , $ν = 0, 1, 2, \dots$
S18GKF	Bessel function of the 1st kind $J_{α \pm n} (z)$
S19AAF	Kelvin function $ber x$
S19ABF	Kelvin function $bei x$
S19ACF	Kelvin function $\ker x$
S19ADF	Kelvin function $kei x$
S19ANF	Kelvin function vectorized $ber x$
S19APF	Kelvin function vectorized $bei x$
S19AQF	Kelvin function vectorized $\ker x$
S19ARF	Kelvin function vectorized $kei x$
S20ACF	Fresnel integral $S (x)$
S20ADF	Fresnel integral $C (x)$
S20AQF	Fresnel integral vectorized $S (x)$
S20ARF	Fresnel integral vectorized $C (x)$
S21BAF	Degenerate symmetrised elliptic integral of 1st kind $R_{C} (x, y)$
S21BBF	Symmetrised elliptic integral of 1st kind $R_{F} (x, y, z)$
S21BCF	Symmetrised elliptic integral of 2nd kind $R_{D} (x, y, z)$
S21BDF	Symmetrised elliptic integral of 3rd kind $R_{J} (x, y, z, r)$
S21BEF	Elliptic integral of 1st kind, Legendre form, $F (ϕ ∣ m)$
S21BFF	Elliptic integral of 2nd kind, Legendre form, $E (ϕ ∣ m)$
S21BGF	Elliptic integral of 3rd kind, Legendre form, $Π (n; ϕ ∣ m)$
S21BHF	Complete elliptic integral of 1st kind, Legendre form, $K (m)$
S21BJF	Complete elliptic integral of 2nd kind, Legendre form, $E (m)$
S21CAF	Jacobian elliptic functions sn, cn and dn of real argument
S21CBF	Jacobian elliptic functions sn, cn and dn of complex argument
S21CCF	Jacobian theta functions $θ_{k} (x, q)$ of real argument
S21DAF	General elliptic integral of 2nd kind $F (z, k^{'}, a, b)$ of complex argument
S22AAF	Legendre functions of 1st kind $P_{n}^{m} (x)$ or $\bar{P_{n}^{m}} (x)$
S22BAF	Real confluent hypergeometric function ${}_{1}F_{1} (a; b; x)$
S22BBF	Real confluent hypergeometric function ${}_{1}F_{1} (a; b; x)$ in scaled form
S30AAF	Black–Scholes–Merton option pricing formula
S30ABF	Black–Scholes–Merton option pricing formula with Greeks
S30BAF	Floating-strike lookback option pricing formula
S30BBF	Floating-strike lookback option pricing formula with Greeks
S30CAF	Binary option, cash-or-nothing pricing formula
S30CBF	Binary option, cash-or-nothing pricing formula with Greeks
S30CCF	Binary option, asset-or-nothing pricing formula
S30CDF	Binary option, asset-or-nothing pricing formula with Greeks
S30FAF	Standard barrier option pricing formula
S30JAF	Jump-diffusion, Merton's model, option pricing formula
S30JBF	Jump-diffusion, Merton's model, option pricing formula with Greeks
S30NAF	Heston's model option pricing formula
S30NBF	Heston's model option pricing formula with Greeks
S30QCF	American option, Bjerksund and Stensland pricing formula
S30SAF	Asian option, geometric continuous average rate pricing formula
S30SBF	Asian option, geometric continuous average rate pricing formula with Greeks

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Keyword Index for the NAG Library Manual

NAG Library Manual