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<title>MathGL 2.1.2: 3.6 Textual formulas</title>
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<a name="Textual-formulas-1"></a>
<h2 class="section">3.6 Textual formulas</h2>
<a name="index-Textual-formulas"></a>
<p>MathGL have the fast variant of textual formula evaluation
(see section <a href="mathgl_en_63.html#Evaluate-expression">Evaluate expression</a>)
. There are a lot of functions and operators available. The operators are: ‘<samp>+</samp>’ – addition, ‘<samp>-</samp>’ – subtraction, ‘<samp>*</samp>’ – multiplication, ‘<samp>/</samp>’ – division, ‘<samp>^</samp>’ – integer power. Also there are logical “operators”: ‘<samp><</samp>’ – true if x<y, ‘<samp>></samp>’ – true if x>y, ‘<samp>=</samp>’ – true if x=y, ‘<samp>&</samp>’ – true if x and y both nonzero, ‘<samp>|</samp>’ – true if x or y nonzero. These logical operators have lowest priority and return 1 if true or 0 if false.
</p>
<p>The basic functions are: ‘<samp>sqrt(x)</samp>’ – square root of <var>x</var>, ‘<samp>pow(x,y)</samp>’ – power <var>x</var> in <var>y</var>, ‘<samp>ln(x)</samp>’ – natural logarithm of <var>x</var>, ‘<samp>lg(x)</samp>’ – decimal logarithm of <var>x</var>, ‘<samp>log(a,x)</samp>’ – logarithm base <var>a</var> of <var>x</var>, ‘<samp>abs(x)</samp>’ – absolute value of <var>x</var>, ‘<samp>sign(x)</samp>’ – sign of <var>x</var>, ‘<samp>mod(x,y)</samp>’ – x modulo y, ‘<samp>step(x)</samp>’ – step function, ‘<samp>int(x)</samp>’ – integer part of <var>x</var>, ‘<samp>rnd</samp>’ – random number, ‘<samp>pi</samp>’ – number
π = 3.1415926…</p>
<p>Trigonometric functions are: ‘<samp>sin(x)</samp>’, ‘<samp>cos(x)</samp>’, ‘<samp>tan(x)</samp>’ (or ‘<samp>tg(x)</samp>’). Inverse trigonometric functions are: ‘<samp>asin(x)</samp>’, ‘<samp>acos(x)</samp>’, ‘<samp>atan(x)</samp>’. Hyperbolic functions are: ‘<samp>sinh(x)</samp>’ (or ‘<samp>sh(x)</samp>’), ‘<samp>cosh(x)</samp>’ (or ‘<samp>ch(x)</samp>’), ‘<samp>tanh(x)</samp>’ (or ‘<samp>th(x)</samp>’). Inverse hyperbolic functions are: ‘<samp>asinh(x)</samp>’, ‘<samp>acosh(x)</samp>’, ‘<samp>atanh(x)</samp>’.
</p>
<p>There are a set of special functions: ‘<samp>gamma(x)</samp>’ – Gamma function Γ(x) = ∫<sub>0</sub><sup>∞</sup> t<sup>x-1</sup> exp(-t) dt, ‘<samp>psi(x)</samp>’ – digamma function ψ(x) = Γ′(x)/Γ(x) for x≠0, ‘<samp>ai(x)</samp>’ – Airy function Ai(x), ‘<samp>bi(x)</samp>’ – Airy function Bi(x), ‘<samp>cl(x)</samp>’ – Clausen function, ‘<samp>li2(x)</samp>’ (or ‘<samp>dilog(x)</samp>’) – dilogarithm Li<sub>2</sub>(x) = -ℜ∫<sub>0</sub><sup>x</sup>ds log(1-s)/s, ‘<samp>sinc(x)</samp>’ – compute sinc(x) = sin(πx)/(πx) for any value of x, ‘<samp>zeta(x)</samp>’ – Riemann zeta function ζ(s) = ∑<sub>k=1</sub><sup>∞</sup>k<sup>-s</sup> for arbitrary s≠1, ‘<samp>eta(x)</samp>’ – eta function η(s) = (1 - 2<sup>1-s</sup>)ζ(s) for arbitrary s, ‘<samp>lp(l,x)</samp>’ – Legendre polynomial P<sub>l</sub>(x), (|x|≤1, l≥0), ‘<samp>w0(x)</samp>’ – principal branch of the Lambert W function, ‘<samp>w1(x)</samp>’ – principal branch of the Lambert W function. Function W(x) is defined to be solution of the equation: W exp(W) = x. </p>
<p>The exponent integrals are: ‘<samp>ci(x)</samp>’ – Cosine integral Ci(x) = ∫<sub>0</sub><sup>x</sup>dt cos(t)/t, ‘<samp>si(x)</samp>’ – Sine integral Si(x) = ∫<sub>0</sub><sup>x</sup>dt sin(t)/t, ‘<samp>erf(x)</samp>’ – error function erf(x) = (2/√π) ∫<sub>0</sub><sup>x</sup>dt exp(-t<sup>2</sup>) , ‘<samp>ei(x)</samp>’ – exponential integral Ei(x) = -PV(∫<sub>-x</sub><sup>∞</sup>dt exp(-t)/t) (where PV denotes the principal value of the integral), ‘<samp>e1(x)</samp>’ – exponential integral E<sub>1</sub>(x) = ℜ∫<sub>1</sub><sup>∞</sup>dt exp(-xt)/t, ‘<samp>e2(x)</samp>’ – exponential integral E<sub>2</sub>(x) = ℜ∫<sub>1</sub>∞</sup>dt exp(-xt)/t<sup>2</sup>, ‘<samp>ei3(x)</samp>’ – exponential integral Ei<sub>3</sub>(x) = ∫<sub>0</sub><sup>x</sup>dt exp(-t<sup>3</sup>) for x≥0. </p>
<p>Bessel functions are: ‘<samp>j(nu,x)</samp>’ – regular cylindrical Bessel function of fractional order <em>nu</em>, ‘<samp>y(nu,x)</samp>’ – irregular cylindrical Bessel function of fractional order <em>nu</em>, ‘<samp>i(nu,x)</samp>’ – regular modified Bessel function of fractional order <em>nu</em>, ‘<samp>k(nu,x)</samp>’ – irregular modified Bessel function of fractional order <em>nu</em>. </p>
<p>Elliptic integrals are: ‘<samp>ee(k)</samp>’ – complete elliptic integral is denoted by E(k) = E(π/2,k), ‘<samp>ek(k)</samp>’ – complete elliptic integral is denoted by K(k) = F(π/2,k), ‘<samp>e(phi,k)</samp>’ – elliptic integral E(φ,k) = ∫<sub>0</sub><sup>φ</sup>dt √(1 - k<sup>2</sup>sin<sup>2</sup>(t)), ‘<samp>f(phi,k)</samp>’ – elliptic integral F(φ,k) = ∫<sub>0</sub><sup>φ</sup>dt 1/√(1 - k<sup>2</sup>sin<sup>2</sup>(t))</p>
<p>Jacobi elliptic functions are: ‘<samp>sn(u,m)</samp>’, ‘<samp>cn(u,m)</samp>’, ‘<samp>dn(u,m)</samp>’, ‘<samp>sc(u,m)</samp>’, ‘<samp>sd(u,m)</samp>’, ‘<samp>ns(u,m)</samp>’, ‘<samp>cs(u,m)</samp>’, ‘<samp>cd(u,m)</samp>’, ‘<samp>nc(u,m)</samp>’, ‘<samp>ds(u,m)</samp>’, ‘<samp>dc(u,m)</samp>’, ‘<samp>nd(u,m)</samp>’.
</p>
<p>Note, some of these functions are unavailable if MathGL was compiled without GSL support.
</p>
<p>There is no difference between lower or upper case in formulas. If argument value lie outside the range of function definition then function returns NaN.
</p>
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