# Various functions taken from the Wolfram Functions Site ```r w07.23.06.0026.01(A, n, m, z, tol = 0, maxiter = 2000, method = "a") w07.23.06.0026.01_bit1(A, n, m, z, tol = 0) w07.23.06.0026.01_bit2(A, n, m, z, tol = 0, maxiter = 2000) w07.23.06.0026.01_bit3_a(A, n, m, z, tol = 0) w07.23.06.0026.01_bit3_b(A, n, m, z, tol = 0) w07.23.06.0026.01_bit3_c(A, n, m, z, tol = 0) w07.23.06.0029.01(A, n, m, z, tol = 0, maxiter = 2000) w07.23.06.0031.01(A, n, m, z, tol = 0, maxiter = 2000) w07.23.06.0031.01_bit1(A, n, m, z, tol = 0, maxiter = 2000) w07.23.06.0031.01_bit2(A, n, m, z, tol = 0, maxiter = 2000) ``` ## Arguments - `A`: Parameter of hypergeometric function - `m,n`: Integers - `z`: Primary complex argument - `tol,maxiter`: Numerical arguments as per `genhypergeo()` - `method`: Character, specifying method to be used ## Details The `method` argument is described at `f15.3.10`. All functions' names follow the conventions in `Hypergeometric2F1.pdf`. * Function `w07.23.06.0026.01(A, n, m, z)` returns $hypergeo(A,A+n,A+m,z)$ where $m$ and $n$ are nonnegative integers with $m\>=n$. * Function `w07.23.06.0029.01(A, n, m, z)` returns $hypergeo(A,A+n,A-m,z)$. * Function `w07.23.06.0031.01(A, n, m, z)` returns $hypergeo(A,A+n,A-m,z)$ with $m\<=n$. ## Note These functions use the `psigamma()` function which does not yet take complex arguments; this means that complex values for `A` are not supported. I'm working on it. ## References `http://functions.wolfram.com/Hypergeometric2F1.pdf` ## Author(s) Robin K. S. Hankin ## See Also `f15.3.10`,`hypergeo` ## Examples ```r # Here we catch some answers from Maple (jjM) and compare it with R's: jjM <- 0.95437201847068289095 + 0.80868687461954479439i # Maple's answer jjR <- w07.23.06.0026.01(A=1.1 , n=1 , m=4 , z=1+1i) # [In practice, one would type 'hypergeo(1.1, 2.1, 5.1, 1+1i)'] stopifnot(Mod(jjM - jjR) < 1e-10) jjM <- -0.25955090546083991160e-3 - 0.59642767921444716242e-3i jjR <- w07.23.06.0029.01(A=4.1 , n=1 , m=1 , z=1+4i) # [In practice, one would type 'hypergeo(4.1, 3.1, 5.1, 1+1i)'] stopifnot(Mod(jjM - jjR) < 1e-15) jjM <- 0.33186808222278923715e-1 - 0.40188208572232037363e-1i jjR <- w07.23.06.0031.01(6.7,2,1,2+1i) # [In practice, one would type 'hypergeo(6.7, 8.7, 7.7, 2+1i)'] stopifnot(Mod(jjM - jjR) < 1e-10) ```

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