DiscreteShift (Built-in Mathematica Symbol)

DiscreteShift[f, i] gives the discrete shift DiscreteShift[f(i), i] == f(i + 1). DiscreteShift[f, {i, n}] gives the multiple shift \[DiscreteShift]_i^n\ f.DiscreteShift[f, ...

Further Examples of Exactly Solvable ... (Mathematica Tutorial)

The solutions to many second-order ODEs can be expressed in terms of special functions. Solutions to certain higher-order ODEs can also be expressed using AiryAi, BesselJ, ...

PolyGamma (Built-in Mathematica Symbol)

PolyGamma[z] gives the digamma function \[Psi](z). PolyGamma[n, z] gives the n\[Null]^th derivative of the digamma function \[Psi] (n) (z).

Csc (Built-in Mathematica Symbol)

Csc[z] gives the cosecant of z.

SoundNote (Built-in Mathematica Symbol)

SoundNote[pitch] represents a music-like sound note with the specified pitch.SoundNote[pitch, t] takes the note to have duration t.SoundNote[pitch, {t_min, t_max}] takes the ...

Sums and Products (Mathematica Tutorial)

This constructs the sum ∑_(i=1)^7 (x^i)/(i) . You can leave out the lower limit if it is equal to 1. This makes i increase in steps of 2, so that only odd-numbered values are ...

ArcCos (Built-in Mathematica Symbol)

ArcCos[z] gives the arc cosine cos -1 (z) of the complex number z.

ArcSin (Built-in Mathematica Symbol)

ArcSin[z] gives the arc sine sin -1 (z) of the complex number z.

Rigid Body Solvers (Mathematica Tutorial)

The equations of motion for a free rigid body whose center of mass is at the origin are given by the following Euler equations (see [MR99]). Two quadratic first integrals of ...

ArcCsc (Built-in Mathematica Symbol)

ArcCsc[z] gives the arc cosecant csc -1 (z) of the complex number z.