Fungrim symbol: HurwitzZeta

Symbol: HurwitzZeta —

\zeta\!\left(s, a\right)

— Hurwitz zeta function

►HurwitzZeta(s, a) —

\zeta\!\left(s, a\right)

— represents the Hurwitz zeta function of argument

s

and parameter

a

►HurwitzZeta(s, a, 1) —

\zeta'\!\left(s, a\right)

— represents the Hurwitz zeta function of argument

s

and parameter

a

, differentiated once with respect to

s

►HurwitzZeta(s, a, r) —

\zeta^{(r)}\!\left(s, a\right)

— represents the Hurwitz zeta function of argument

s

and parameter

a

, differentiated to order

r

with respect to

s

References:

https://dlmf.nist.gov/25.11
http://functions.wolfram.com/ZetaFunctionsandPolylogarithms/Zeta2/

Definitions:

Fungrim symbol	Notation	Short description
`HurwitzZeta`	$\zeta\!\left(s, a\right)$	Hurwitz zeta function

Source code for this entry:

Entry(ID("04217b"),
    SymbolDefinition(HurwitzZeta, HurwitzZeta(s, a), "Hurwitz zeta function"),
    CodeExample(HurwitzZeta(s, a), "represents the Hurwitz zeta function of argument", s, "and parameter", a, "."),
    CodeExample(HurwitzZeta(s, a, 1), "represents the Hurwitz zeta function of argument", s, "and parameter", a, ", differentiated once with respect to", s, "."),
    CodeExample(HurwitzZeta(s, a, r), "represents the Hurwitz zeta function of argument", s, "and parameter", a, ", differentiated to order", r, "with respect to", s, "."),
    References("https://dlmf.nist.gov/25.11", "http://functions.wolfram.com/ZetaFunctionsandPolylogarithms/Zeta2/"))

Topics using this symbol

The symbol HurwitzZeta appears in 8 topics:

Hurwitz zeta function (in 80 entries)
Dirichlet L-functions (in 5 entries)
Digamma function (in 2 entries)
Stieltjes constants (in 1 entries)
Specific values of the digamma function (in 1 entries)
Catalan's constant (in 1 entries)
Bernoulli numbers and polynomials (in 1 entries)
Barnes G-function (in 1 entries)

Entries using this symbol

The symbol HurwitzZeta appears in 84 entries: