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> require(hypergeo)
Loading required package: hypergeo
> #  First some test values for z, generated randomly.  These values are
> #  selected so as to use each of the subfunctions of hypergeom():
> 
> z <-
+   c(
+     0.28 - 0.21i,
+    -0.79 - 0.40i,
+     0.56 + 0.05i,
+     2.13 + 0.68i, 
+    -0.43 - 1.47i,
+     1.23 + 0.48i
+     )
> 
> # First test:  some randomly chosen values for A,B,C; my package:
> my.ans <- hypergeo(A=1.21,B=1.443,C=1.88,z=z)
> 
> # Compare with Maple's:
> maple.ans <-
+   c(
+     1.26242625279896547050 - 0.33515733250598455101i  ,
+     0.55218026726586346626 - 0.11826012518395685586i  ,
+     2.08656513655255552950 + 0.21074089910422408972i  ,
+    -0.71334498434004598167 + 0.59647479085505445853i  ,
+     0.36911468617705947291 - 0.35906488952504313903i  ,
+    -0.44806924103752606401 + 1.91140611055324833040i
+     )
> 
> 
> 
> stopifnot(all(Mod(my.ans-maple.ans) < 1e-9))
> 
> 
> # Now verify eqn 15.1.15, p556:
> "eqn15.1.15a" <- function(a,z){
+   hypergeo(A=a, B=1-a, C=3/2, z=sin(z)^2,tol=1e-9)
+ }
> 
> "eqn15.1.15b" <- function(a,z){sin((2*a-1)*z)/((2*a-1)*sin(z))}
> 
> Mod(eqn15.1.15a(0.2,z)-eqn15.1.15b(0.2,z)) # Observe the mismatch for
[1] 4.703149e-16 1.129823e-09 9.367538e-11 9.319110e-01 5.083351e-11
[6] 2.909044e-15
>                                            # element 4.  BUT
>                                            # hypergeo() agrees with
>                                            # Maple, which gives
>                                            # 1.038571815 - 0.1598166166i
> 
> 
> 
> "eqn15.2.10" <- function(A,B,C,z){    # page 558
+   (C-A)*hypergeo(A-1,B,C,z) + (2*A-C-A*z+B*z)*hypergeo(A,B,C,z) + A*(z-1)*hypergeo(A+1,B,C,z)
+ }
> 
> stopifnot(all(Mod(eqn15.2.10(0.1,0.44,0.611,z))<1e-6))
> 
> 
> ## Now some special elementary cases, on page 556.  Here, "rhs" means
> ## "right hand side" and "lhs" means "left hand side".
> 
> "f15.1.3" <- function(z){
+   lhs <- hypergeo(1,1,2,z)
+   rhs <- -log(1-z)/z
+   return(rhs-lhs)
+ }
> 
> "f15.1.4" <- function(z){
+   lhs <- hypergeo(1/2,1,3/2,z^2)
+   rhs <- 0.5*log((1+z)/(1-z))/z
+   return(rhs-lhs)
+ }
> 
> "f15.1.5" <- function(z){
+   lhs <- hypergeo(1/2,1,3/2,-z^2)
+   rhs <- atan(z)/z
+   return(rhs-lhs)
+ }
> 
> "f15.1.6a" <- function(z){
+   lhs <- hypergeo(1/2,1/2,3/2,z^2)
+   rhs <-  sqrt(1-z^2)*hypergeo(1,1,3/2,z^2)
+   return(rhs-lhs)
+ }
> 
> "f15.1.6b" <- function(z){
+   lhs <- hypergeo(1/2,1/2,3/2,z^2)
+   rhs <- asin(z)/z
+   return(rhs-lhs)
+ }
> 
> "f15.1.7a" <- function(z){
+   lhs <- hypergeo(1/2,1/2,3/2,-z^2)
+   rhs <- sqrt(1+z^2)*hypergeo(1,1,3/2,-z^2)
+   return(rhs-lhs)
+ }
> 
> "f15.1.7b" <- function(z){
+   lhs <- hypergeo(1/2,1/2,3/2,-z^2)
+   rhs <- log(z+sqrt(1+z^2))/z
+   return(rhs-lhs)
+ }
> 
> f.all <- function(z){
+   cbind(
+     f15.1.3 (z),
+     f15.1.4 (z),
+     f15.1.5 (z),
+     f15.1.6a(z),
+     f15.1.6b(z),
+     f15.1.7a(z),
+     f15.1.7b(z)
+     )
+ }
>     
> stopifnot(max(Mod(f.all(z))) < 1e-10)
> 
> 
> 
> # Below, jjR means value obtained from R via the package, and jjM means the value given by maple.
> 
> # Following test fails sometimes.  It passes on my mac, fails on the linuxbox:
> jjR <- genhypergeo_contfrac_single(U=0.2 , L=c(9.9,2.7,8.7) , z=1+10i)
> jjM <- 1.0007289707983569879 + 0.86250714217251837317e-2i
> stopifnot(Mod(jjR-jjM)<1e-10)
> 
> # Test hypergeo_cover1():
> jjR <- hypergeo(pi,pi/2,3*pi/2-4, z=0.1+0.2i)  # ie negative m;  ie f15.3.12()
> jjM <- 0.53745229690249593045 + 1.8917456473240515664i
> stopifnot(Mod(jjR-jjM)<1e-10)
> 
> jjR <- hypergeo(pi,pi/2,3*pi/2-4, z=10.1+0.2i)  # another negative m
> jjM <- 0.31486642443024026933e-2 + 0.10505111398350790590e-2i
> stopifnot(Mod(jjR-jjM)<1e-10)
> 
> jjR <- hypergeo(pi,pi/2,3*pi/2, z=0.1+0.2i)  # m=0 (ie 15.3.10)
> jjM <- 1.0654685003741342889 +0.24452141417139649656i
> stopifnot(Mod(jjR-jjM)<1e-10)
> 
> jjR <- hypergeo(pi,pi/2,3*pi/2+4, z=10.1+0.2i)  # This is positive m (15.3.11)
> jjM <- -0.29639970263878733845 - 0.34765230143995441172i
> stopifnot(Mod(jjR-jjM)<1e-10)
> 
> jjR <- hypergeo(pi,pi/2,3*pi/2+4, z=10.1+0.2i)  # m>0
> jjM <- -0.29639970263878733845 -0.34765230143995441172i
> stopifnot(Mod(jjR-jjM)<1e-10)
> 
> jjM <- -0.90818366414720846181e-2 - 0.10746858256201734833i
> jjR <- hypergeo(pi,pi/2,3*pi/2, z=10.1+0.2i)  # m=0
> stopifnot(Mod(jjR-jjM)<1e-10)
> 
> 
> # Test hypergeo_cover2():
> jjM <- -0.15888831928748121465e-5 + 0.40339599711492215912e-4i
> jjR <- hypergeo(pi,pi+2, 1.1 , 1+10i)
> stopifnot(Mod(jjR-jjM)<1e-10)
> 
> 
> # Test hypergeo_cover3()
> jjM <- -0.24397135980533720308e-1 + 0.28819643319432922231i
> jjR <- hypergeo(pi, 1.4, pi+4,1+6i)
> stopifnot(Mod(jjR-jjM)<1e-10)
> 
> jjM <- -0.10592465301475818414e-1 - 0.15993048891187879153e-1i
> jjR <- hypergeo(pi , pi+1 , pi + 3 , 1+6i)
> stopifnot(Mod(jjR-jjM)<1e-10)
> 
> # Test for hypergeo_taylor():
> jjR <- hypergeo(pi,-4,2.2,1+5i)
> jjM <- 1670.8287595795885335 - 204.81995157365381258i
> stopifnot(Mod(jjR-jjM)<1e-10)
> 
> 
> # quick test for a bug reported by Igor Kojanov
> 
> options(warn=2)
> ignore <- hypergeo(1,2,3,0)
> ignore <- hypergeo(1,1.64,2.64,-0.1111)
> 
> 
> # another test for a bug reported by John Ormerod, following my
> # ill-considered change from gamma(x)*gamma(y)/gamma(z) to
> # exp(lgamma(x)+lgamma(y)-lgamma(z)).  Now using the much superior
> # .f3() and .f4() notation.
> 
> ## MMA> N[Hypergeometric2F1[525/100,1,65/10,501/1000],30]
> ## Out[6]= 1.70239432012007391092082702795
> 
> 
> jjR <- hypergeo(5.25,1,6.5,0.501)
> jj_Mathematica <- 1.70239432012007391092082702795
> stopifnot(Mod(jjR-jj_Mathematica) < 1e-10)
> 
> 
> 
> 
> 
> 
>  ## another test for a typo I corrected:
> 
> 
>  A <- 1
>  B <- 3
>  m <- 2
> jj_R1 <- hypergeo(A,B,A+B+m,0.9+0.01i)
> jj_R2 <- f15.3.11(A,B,m,0.9+0.01i)
> 
> mma_string <- 'N[Hypergeometric2F1[1,3,1+3+2,9/10+I/100],30]'
> jj_mathematica <- 2.04925816767572859287575551415 + 0.03163091033158608113987207436i
> stopifnot(abs(jj_R1-jj_mathematica) < 1e-10)
> stopifnot(abs(jj_R2-jj_mathematica) < 1e-10)
> 
> 
> proc.time()
   user  system elapsed 
   0.25    0.06    0.29