- a\to \infty } . The
Lerch transcendent is
implemented as
LerchPhi in
Maple and Mathematica, and as
lerchphi in
mpmath and SymPy.
Lerch,
Mathias (1887), "Note...
- when
Zwegers discovered the
relation with non-holomorphic
modular forms,
Lerch sums, and
indefinite theta series.
Zwegers showed,
using the
previous work...
-
artificial earth satellites,
Israel program for
Scientific Translations (1967)
Lerch, F.J., Wagner, C.A., Smith, D.E., Sandson, M.L., Brownd, J.E., Richardson...
- {x}{2}}\right)}{2\Gamma (1-x)}}={\frac {\
Phi \left(-1,1,-x\right)}{\Gamma (-x)}}}
where Φ {\displaystyle \
Phi } is the
Lerch zeta function. We also have the Luschny...
- case of the
Lerch transcendent, and is
given by χ ν ( z ) = 2 − ν z Φ ( z 2 , ν , 1 / 2 ) . {\displaystyle \chi _{\nu }(z)=2^{-\nu }z\,\
Phi (z^{2},\nu...
- {x}{2}}\right)}{2\Gamma (1-x)}}={\frac {\
Phi \left(-1,1,-x\right)}{\Gamma (-x)}}}
where Φ {\displaystyle \
Phi } is the
Lerch zeta function, and as H ( x ) = Γ...
- can also be
written in
terms of the
Lerch transcendent Φ ( z , s , a ) = ∑ n = 0 ∞ z n ( n + a ) s : {\textstyle \
Phi (z,s,a)=\sum _{n=0}^{\infty }{\frac...
- cubes". arXiv:1604.07746 [math.NT]. Dobson, J. B. (1
April 2017), "On
Lerch's formula for the
Fermat quotient", p. 23, arXiv:1103.3907v6 [math.NT] Ribenboim...
- definition, in
terms of the
Lerch transcendent, is: β ( s ) = 2 − s Φ ( − 1 , s , 1 2 ) , {\displaystyle \beta (s)=2^{-s}\
Phi \left(-1,s,{{1} \over {2}}\right)...
-
imaginary part of Lis(eiθ). The
Lerch transcendent is
given by Φ ( z , s , q ) = ∑ k = 0 ∞ z k ( k + q ) s {\displaystyle \
Phi (z,s,q)=\sum _{k=0}^{\infty...
