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Feature: polylogarithms with half integer order #17

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Feature: polylogarithms with half integer order #17

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@Expander Expander self-assigned this Sep 17, 2022
@Expander Expander added the enhancement New feature or request label Sep 17, 2022
@Expander
adding stub for half integer Re[Li]
882b137
@Expander
implement even orders
54d74ce
@Expander
implement naive series expansion
7dc98c5
@Expander
implement gamma(n/2)
42aeb73
@Expander
implement zeta function for half-integer arguments
c882e74
@Expander
extend range of zetahalf
bde03de
@Expander
implement first version of expansion near z ~ 1
937cd39
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return correct +/- Inf
1a02ecc
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adding commented test for lihalf_series_unity_pos(n, z)
17aae12
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return zeta(n/2) for x == 1
5a95177
@Expander
move gamma term to the front
4a8e1ab
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correcting comment
4896976
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Li_{1/2}(1) = Inf
e7ac5c1
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extend tests
046f66a
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test case n == 1
666f15c
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indent all zeta values with exponential form
aa3dd78
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indent remaining zeta values
5db8144
@Expander
adding stub for compler lihalf
b659aec
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update test data
5f6e76b
@Expander
update tests
6cb688c
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slighly optimize duplication formula
3c5a31d
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split function
6e746f1
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use more generic one
9f805ec
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implement inversion formula for s = n/2 with n = 1, 3, 5, ...
a312b56
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allow for SpecialFunctions 0.10
c4c0dc6
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extract zeta(s,a) from SpecialFunctions.jl
16c3088 
Note: will not be used in the end
@Expander
extend range for gammahalf(n)
a8c0d5b
@Expander
improve formatting
874e648
@Expander
test special cases a = -1, 0, 1, 2
3d3e539
@Expander
replace division by multiplication
6078540
@Expander
optimize prefactor
34dba16
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specialize input types
5e8954d
@Expander
shorten return statement
2e94aef
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avoid if statement
ef17194
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remove unused function
a7441a1
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rename function
d2728b1
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rename variables
613c5e9
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rename variable
8b84aa3
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merge functions
9b1e3c5
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avoid greek symbols
9c76696
@Expander
remove unused comments
37176d8
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restrict zetahalf to odd integers
8a1e311
@Expander
simplify interface to use rational numbers
86e7655
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fix typo
e5bca09
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compactify test
edbe9cc
@Expander
split test
cb7d73e
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avoid code duplication
c769afe
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reduce nesting
6ed52f5
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more specific error message
e499dbc
@Expander
use a struct to store the test data
7e39a45
@Expander
move struct to top-level scope
ed9f1a3
@Expander
increase test precision for s = 1//2
1f1c450
@Expander
increase test precision
29d0dce
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