S Chapter Contents

S Introduction

s01ba – ln((1+x))

s01ea – Complex exponential, e^z

s07aa – tan(x)

s09aa – arcsin(x)

s09ab – arccos(x)

s10aa – tanh(x)

s10ab – sinh(x)

s10ac – cosh(x)

s11aa – arctanh(x)

s11ab – arcsinh(x)

s11ac – arccosh(x)

s13aa – Exponential integral E_1(x)

s13ac – Cosine integral Ci((x))

s13ad – Sine integral Si((x))

s14aa – Gamma function

s14ab – Log Gamma function

s14ac – psi (x)-ln(x)

s14ad – Scaled derivatives of psi (x)

s14ae – Polygamma function psi ^(n)(x) for real x

s14af – Polygamma function psi ^(n)(z) for complex z

s14ag – Logarithm of the Gamma function ln( Gamma )(z)

s14ba – Incomplete Gamma functions P(ax) and Q(ax)

s15ab – Cumulative Normal distribution function P(x)

s15ac – Complement of cumulative Normal distribution function Q(x)

s15ad – Complement of error function erfc((x))

s15ae – Error function erf((x))

s15af – Dawson's integral

s15dd – Scaled complex complement of error function, exp((-z^2))erfc((-iz))

s17ac – Bessel function Y_0(x)

s17ad – Bessel function Y_1(x)

s17ae – Bessel function J_0(x)

s17af – Bessel function J_1(x)

s17ag – Airy function Ai((x))

s17ah – Airy function Bi((x))

s17aj – Airy function Ai^'((x))

s17ak – Airy function Bi'((x))

s17al – Zeros of Bessel functions J_ alpha (x), J_ alpha '(x), Y_ alpha (x) or Y_ alpha '(x)

s17dc – Bessel functions Y_ nu +a(z), real a >= 0, complex z, nu =0,1,2, ...

s17de – Bessel functions J_ nu +a(z), real a >= 0, complex z, nu =0,1,2, ...

s17dg – Airy functions Ai((z)) and Ai'((z)), complex z

s17dh – Airy functions Bi((z)) and Bi'((z)), complex z

s17dl – Hankel functions H_ nu +a^(j)(z), j=1,2, real a >= 0, complex z, nu =0,1,2, ...

s18ac – Modified Bessel function K_0(x)

s18ad – Modified Bessel function K_1(x)

s18ae – Modified Bessel function I_0(x)

s18af – Modified Bessel function I_1(x)

s18cc – Scaled modified Bessel function e^xK_0(x)

s18cd – Scaled modified Bessel function e^xK_1(x)

s18ce – Scaled modified Bessel function e^-|x|I_0(x)

s18cf – Scaled modified Bessel function e^-|x|I_1(x)

s18dc – Modified Bessel functions K_ nu +a(z), real a >= 0, complex z, nu =0,1,2, ...

s18de – Modified Bessel functions I_ nu +a(z), real a >= 0, complex z, nu =0,1,2, ...

s18gk – Bessel function of the 1st kind J_ alpha ±n(z)

s19aa – Kelvin function ber(x)

s19ab – Kelvin function bei(x)

s19ac – Kelvin function ker(x)

s19ad – Kelvin function kei(x)

s20ac – Fresnel integral S(x)

s20ad – Fresnel integral C(x)

s21ba – Degenerate symmetrised elliptic integral of 1st kind R_C(xy)

s21bb – Symmetrised elliptic integral of 1st kind R_F(xyz)

s21bc – Symmetrised elliptic integral of 2nd kind R_D(xyz)

s21bd – Symmetrised elliptic integral of 3rd kind R_J(xyzr)

s21ca – Jacobian elliptic functions sn, cn and dn of real argument

s21cb – Jacobian elliptic functions sn, cn and dn of complex argument

s21cc – Jacobian theta functions theta _k(xq) of real argument

s21da – General elliptic integral of 2nd kind F(zk'ab) of complex argument

s22aa – Legendre functions of 1st kind P_n^m(x) or (P_n^m)^-(x)