Fungrim symbol: Step

Symbol: Step —

f(a), f\!\left(a + 1\right), \ldots, f(b)

— Enumerated sequence

Step(f(n), For(n, a, b)) represents the sequence of values

f(n)

for

n

between the integers

a

and

b

. The sequence is empty if

b < a

. This expression does not represent a mathematical object: it only exists at the expression level, and injects the sequence between a surrounding arguments. To construct a mathematical object, we must pass the generator expression to a function such as Tuple. Examples:

f(Step(Pow(k, 2), For(k, 1, 10)))

f\!\left({1}^{2}, {2}^{2}, \ldots, {10}^{2}\right)

Tuple(Step(Repeat(n, n), For(n, 0, N)))

\left(\underbrace{0, \ldots, 0}_{0 \text{ times}}, \underbrace{1, \ldots, 1}_{1 \text{ times}}, \ldots, \underbrace{N, \ldots, N}_{N \text{ times}}\right)

Tuple(1, 2, 2, Step(Repeat(n, n), For(n, 3, N)))

\left(1, 2, 2, \underbrace{3, \ldots, 3}_{3 \text{ times}}, \underbrace{4, \ldots, 4}_{4 \text{ times}}, \ldots, \underbrace{N, \ldots, N}_{N \text{ times}}\right)

Definitions:

Fungrim symbol	Notation	Short description
`Pow`	${a}^{b}$	Power

Source code for this entry:

Entry(ID("73f5e7"),
    SymbolDefinition(Step, Step(f(n), For(n, a, b)), "Enumerated sequence"),
    Description(SourceForm(Step(f(n), For(n, a, b))), " represents the sequence of values ", f(n), "for ", n, "between ", "the integers", a, "and", b, ". ", "The sequence is empty if ", Less(b, a), ". ", "This expression does not represent ", "a mathematical object: it only exists at the expression level, and ", "injects the sequence between a surrounding arguments. ", "To construct a mathematical object, we must pass the generator expression ", "to a function such as", SourceForm(Tuple), ". Examples: "),
    Description(SourceForm(f(Step(Pow(k, 2), For(k, 1, 10))))),
    Description(f(Step(Pow(k, 2), For(k, 1, 10)))),
    Description(SourceForm(Tuple(Step(Repeat(n, n), For(n, 0, N))))),
    Description(Tuple(Step(Repeat(n, n), For(n, 0, N)))),
    Description(SourceForm(Tuple(1, 2, 2, Step(Repeat(n, n), For(n, 3, N))))),
    Description(Tuple(1, 2, 2, Step(Repeat(n, n), For(n, 3, N)))))

Topics using this symbol

The symbol Step appears in 3 topics:

Series representations of Carlson symmetric elliptic integrals (in 2 entries)
Symbolic expressions (in 1 entries)
Multiple zeta values (in 1 entries)

Entries using this symbol

The symbol Step appears in 4 entries: