- 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...
- {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 the
Luschny factorial:...
-
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, and as H ( x ) = Γ...
- 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...
- }}}&{\text{if }}z=1\end{cases}}\end{aligned}}}
where Φ ( ) {\displaystyle \
Phi ()} is the
Lerch transcendent function. In
terms of the
circular variable z = e i...
-
infinite products for some
classical constants via
analytic continuations of
Lerch's transcendent". The
Ramanujan Journal. 16 (3): 247–270. arXiv:math/0506319...
-
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...
- Beat Expos,
Capture East,
Washington Post,
Thomas Boswell,
October 5, 1980.
PHI/PHI198004110.shtml 1980
Opening Day
Lineup at Baseball-Reference
Roger Freed...
