JuliaMath/SpecialFunctions.jl

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• Unexpected passes in Float32 Bessel inference tests on 32-bit Julia

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  Difficulty 2/5 1-3 hours Newbie friendliness 68/100

  JuliaMath/SpecialFunctions.jl#570 · Opened Nov 5, 2026

• Differences ψₙ(x + m) − ψₙ(x) for integer m: subtraction loses up to 9 digits for large x, while the exact finite sum is accurate and about 20× cheaper

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  Difficulty 5/5 Over a week Newbie friendliness 40/100

  JuliaMath/SpecialFunctions.jl#569 · 2 comments · Opened Nov 4, 2026

• gamma(a, x) and loggamma(a, x) throw for every real shape a > 51

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  Difficulty 4/5 3-5 days Newbie friendliness 25/100

  JuliaMath/SpecialFunctions.jl#567 · Opened Nov 2, 2026

• `beta_inc_inv` keeps evaluating `beta_inc` after it has converged

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  Difficulty 4/5 1-2 days Newbie friendliness 56/100

  JuliaMath/SpecialFunctions.jl#563 · Opened Oct 19, 2026

• beta_inc and beta_inc_inv allocate

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  Difficulty 3/5 1-2 days Newbie friendliness 72/100

  JuliaMath/SpecialFunctions.jl#560 · Opened Sep 28, 2026

• `zeta(s)` and `eta(s)` return `NaN` or `Inf` for every real s < `-170.62`

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  Difficulty 4/5 3-5 days Newbie friendliness 48/100

  JuliaMath/SpecialFunctions.jl#556 · Opened Sep 7, 2026

• expint(ν, z) loses 8-17 bits to cancellation; one- and two-argument forms disagree by up to 439 ulps in Float32

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  Difficulty 5/5 Over a week Newbie friendliness 35/100

  JuliaMath/SpecialFunctions.jl#551 · Opened Aug 20, 2026

• expint truncates its series after a number of terms fixed for Float64, silently capping BigFloat accuracy

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  Difficulty 4/5 3-5 days Newbie friendliness 48/100

  JuliaMath/SpecialFunctions.jl#546 · 2 comments · Opened Aug 18, 2026

• expint is inaccurate for Float32/Float16 arguments near the negative real axis

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  Difficulty 4/5 3-5 days Newbie friendliness 55/100

  JuliaMath/SpecialFunctions.jl#545 · 3 comments · Opened Aug 18, 2026

• Implement partial derivative wrt to shape parameter for `gamma_inc` as a convergent series

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  Difficulty 4/5 3-5 days Newbie friendliness 52/100

  JuliaMath/SpecialFunctions.jl#531 · 3 comments · 2 reactions · Opened May 29, 2026

• Add functions for incomplete elliptic integrals

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  Difficulty 5/5 Over a week Newbie friendliness 45/100

  JuliaMath/SpecialFunctions.jl#529 · Opened May 18, 2026

• Merging JacobiElliptic with SpecialFunctions

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  Difficulty 5/5 Over a week Newbie friendliness 25/100

  JuliaMath/SpecialFunctions.jl#511 · 6 comments · Opened Jan 20, 2026

• `beta_inv` and `beta_inv_inc` gradients.

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  Difficulty 4/5 3-5 days Newbie friendliness 42/100

  JuliaMath/SpecialFunctions.jl#505 · 1 reaction · Opened Oct 4, 2025

• `zeta(0, x), zeta(s, -1)` gives wrong answer

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  Difficulty 3/5 1-2 days Newbie friendliness 35/100

  JuliaMath/SpecialFunctions.jl#496 · Opened May 3, 2025

• erf performance regression on Windows

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  dependencies

  Difficulty 4/5 3-5 days Newbie friendliness 35/100

  JuliaMath/SpecialFunctions.jl#495 · 2 comments · Opened Apr 23, 2025

• ForwardDiff of complex `erfcx` fails

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  Difficulty 3/5 1-2 days Newbie friendliness 52/100

  JuliaMath/SpecialFunctions.jl#493 · Opened Apr 13, 2025

• Generalized zeta function cutoff causes discontinuity

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  Difficulty 4/5 3-5 days Newbie friendliness 48/100

  JuliaMath/SpecialFunctions.jl#488 · 1 reaction · Opened Mar 21, 2025

• `NaN` in `digamma` caused by `_cotpi`

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  Difficulty 3/5 1-2 days Newbie friendliness 42/100

  JuliaMath/SpecialFunctions.jl#480 · 2 comments · Opened Nov 9, 2024

• Allocations in the sum over a product of `besselj(::Int64, ::Float32)`

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  Difficulty 3/5 1-2 days Newbie friendliness 42/100

  JuliaMath/SpecialFunctions.jl#472 · Opened May 1, 2024

• Extensive use of abs for complex tolerances

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  Difficulty 4/5 3-5 days Newbie friendliness 42/100

  JuliaMath/SpecialFunctions.jl#468 · 2 comments · Opened Mar 18, 2024

• Internals of the incomplete gamma function does not work with `ForwardDiff.jl`'s `Dual()` type due to enforced floating point precision

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  Difficulty 4/5 3-5 days Newbie friendliness 35/100

  JuliaMath/SpecialFunctions.jl#465 · 4 comments · Opened Feb 19, 2024

• Rewrite all AMOS code in julia

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  enhancement

  Difficulty 5/5 Over a week Newbie friendliness 20/100

  JuliaMath/SpecialFunctions.jl#461 · 5 comments · Opened Jan 18, 2024

• Large negative real number arguments return NaN for expintx

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  Difficulty 4/5 3-5 days Newbie friendliness 35/100

  JuliaMath/SpecialFunctions.jl#457 · 1 comment · Opened Jan 12, 2024

• `expint(nu,z)` has bad precision for `nu != 1`

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  Difficulty 4/5 3-5 days Newbie friendliness 48/100

  JuliaMath/SpecialFunctions.jl#453 · 1 comment · Opened Nov 26, 2023

• What about `gamma_inc_inv`'s derivative ?

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  enhancement

  Difficulty 5/5 Over a week Newbie friendliness 25/100

  JuliaMath/SpecialFunctions.jl#452 · 2 comments · Opened Oct 31, 2023

• Generalize beta, logbeta, etc. to any number of arguments

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  JuliaMath/SpecialFunctions.jl#449 · Opened Oct 12, 2023

• Regularized Kumer Functions?

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  JuliaMath/SpecialFunctions.jl#448 · 1 comment · Opened Sep 25, 2023

• Segfault in besselj

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  Difficulty 4/5 3-5 days Newbie friendliness 35/100

  JuliaMath/SpecialFunctions.jl#446 · 2 comments · Opened Aug 7, 2023

• Reduce/remove inner allocations (e.g. `gamma_inc_taylor`, `gamma_inc_asym`)

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  Difficulty 5/5 Over a week Newbie friendliness 38/100

  JuliaMath/SpecialFunctions.jl#442 · 9 comments · Opened May 3, 2023

• Inverse of erfi

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  Difficulty 4/5 3-5 days Newbie friendliness 35/100

  JuliaMath/SpecialFunctions.jl#441 · Opened Apr 9, 2023

• Address known-broken ChainRules tests

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  Difficulty 3/5 1-2 days Newbie friendliness 25/100

  JuliaMath/SpecialFunctions.jl#439 · Opened Mar 29, 2023

• Add logabsgamma(::Complex)

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  Difficulty 3/5 1-2 days Newbie friendliness 38/100

  JuliaMath/SpecialFunctions.jl#437 · 3 comments · Opened Mar 24, 2023

• Derivative of the generalised zeta function

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  JuliaMath/SpecialFunctions.jl#436 · Opened Mar 23, 2023

• Feature request: Add parabolic cylinder function

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  enhancement

  Difficulty 5/5 Over a week Newbie friendliness 25/100

  JuliaMath/SpecialFunctions.jl#417 · 1 reaction · Opened Dec 16, 2022

• no method matching _erf(::Complex{BigFloat})

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  Difficulty 4/5 3-5 days Newbie friendliness 45/100

  JuliaMath/SpecialFunctions.jl#416 · 4 comments · Opened Dec 12, 2022

• `gamma(0)` returns the wrong value.

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  JuliaMath/SpecialFunctions.jl#411 · 1 comment · Opened Oct 25, 2022

• Generalized zeta function imprecise for large negative s

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  Difficulty 4/5 3-5 days Newbie friendliness 35/100

  JuliaMath/SpecialFunctions.jl#410 · Opened Oct 12, 2022

• switch to Bessels.jl for real bessel functions

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  Difficulty 4/5 3-5 days Newbie friendliness 35/100

  JuliaMath/SpecialFunctions.jl#409 · 25 comments · 8 reactions · Opened Aug 8, 2022

• Add Fresnel integral

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  Difficulty 4/5 3-5 days Newbie friendliness 35/100

  JuliaMath/SpecialFunctions.jl#398 · 1 comment · 3 reactions · Opened Apr 23, 2022

• Add Fermi-Dirac-Integral

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  JuliaMath/SpecialFunctions.jl#395 · 3 comments · Opened Mar 11, 2022

• Debye functions

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  Difficulty 4/5 3-5 days Newbie friendliness 35/100

  JuliaMath/SpecialFunctions.jl#384 · Opened Feb 17, 2022

• `besselk(x, 0im)` fails

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  Difficulty 3/5 1-2 days Newbie friendliness 50/100

  JuliaMath/SpecialFunctions.jl#382 · 5 comments · Opened Feb 10, 2022

• Overflow for besselh(85.5,0.001)

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  Difficulty 4/5 3-5 days Newbie friendliness 35/100

  JuliaMath/SpecialFunctions.jl#381 · 1 comment · Opened Feb 9, 2022

• beta_inc in the degenerate cases

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  Difficulty 5/5 Over a week Newbie friendliness 25/100

  JuliaMath/SpecialFunctions.jl#378 · 4 comments · Opened Feb 4, 2022

• Remove all deprecated functions?

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  Difficulty 5/5 Over a week Newbie friendliness 25/100

  JuliaMath/SpecialFunctions.jl#365 · 1 comment · 1 reaction · Opened Nov 23, 2021

• erfcx(BigFloat) misses a connection segment

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  Difficulty 4/5 3-5 days Newbie friendliness 25/100

  JuliaMath/SpecialFunctions.jl#363 · 5 comments · 1 reaction · Opened Nov 22, 2021

• Complete elliptic integral functions fail on BigFloat

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  Difficulty 4/5 3-5 days Newbie friendliness 25/100

  JuliaMath/SpecialFunctions.jl#362 · Opened Nov 21, 2021

• [Feature Request] Polylogarithm

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  JuliaMath/SpecialFunctions.jl#358 · 4 comments · Opened Oct 28, 2021

• erfinv(::BigFloat) enters infinite loop

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  Difficulty 4/5 3-5 days Newbie friendliness 35/100

  JuliaMath/SpecialFunctions.jl#338 · Opened Aug 1, 2021

• Derivatives of the incomplete gamma functions with respect to parameter `a` are missing

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  Difficulty 5/5 Over a week Newbie friendliness 25/100

  JuliaMath/SpecialFunctions.jl#317 · 13 comments · 1 reaction · Opened May 17, 2021