Kummer

Description

Kummer[i][exp] applies Kummer relation number i (i =1, ... 24, 94,95,96) to all Hypergeometric2F1 in exp. i = 94 corresponds to eq. 9.131.2, i = 95 to eq. 9.132.1 and i = 96 to eq. 9.132.2 in Gradsteyn & Ryzhik.

See also:  HypergeometricAC.

Examples

Hypergeometric2F1[a, b, c, z] == Kummer[2][
        Hypergeometric2F1[a, b, c, z]]

Hypergeometric2F1[a, b, c, z] == Kummer[3][
        Hypergeometric2F1[a, b, c, z]]

Hypergeometric2F1[a, b, c, z] == Kummer[4][
        Hypergeometric2F1[a, b, c, z]]

Hypergeometric2F1[a, b, c, 1 - z] == Kummer[6][
        Hypergeometric2F1[a, b, c, 1 - z]]

Hypergeometric2F1[a, b, a + b + 1 - c, 1 - z] == Kummer[6][
        Hypergeometric2F1[a, b, a + b + 1 - c, 1 - z]]

Hypergeometric2F1[a, b, c, 1 - z] == Kummer[7][
        Hypergeometric2F1[a, b, c, 1 - z]]

Hypergeometric2F1[a, b, a + b + 1 - c, 1 - z] == Kummer[7][
        Hypergeometric2F1[a, b, a + b + 1 - c, 1 - z]]

Hypergeometric2F1[a, b, c, 1 - z] == Kummer[8][
        Hypergeometric2F1[a, b, c, 1 - z]]

Hypergeometric2F1[a, b, a + b + 1 - c, 1 - z] == Kummer[8][
        Hypergeometric2F1[a, b, a + b + 1 - c, 1 - z]]

Hypergeometric2F1[a, b, c, z^(-1)] == Kummer[10][
        Hypergeometric2F1[a, b, c, z^(-1)]]

Hypergeometric2F1[a, a + 1 - c, a + 1 - b, 
        z^(-1)] == Kummer[10][
        Hypergeometric2F1[a, a + 1 - c, a + 1 - b, 
          z^(-1)]]

Hypergeometric2F1[a, b, c, z^(-1)] == Kummer[11][
        Hypergeometric2F1[a, b, c, z^(-1)]]

Hypergeometric2F1[a, a + 1 - c, a + 1 - b, 
        z^(-1)] == Kummer[11][
        Hypergeometric2F1[a, a + 1 - c, a + 1 - b, 
          z^(-1)]]

Hypergeometric2F1[a, b, c, z^(-1)] == Kummer[12][
        Hypergeometric2F1[a, b, c, z^(-1)]]

Hypergeometric2F1[a, a + 1 - c, a + 1 - b, 
        z^(-1)] == Kummer[12][
        Hypergeometric2F1[a, a + 1 - c, a + 1 - b, 
          z^(-1)]]

Hypergeometric2F1[a, b, c, z^(-1)] == Kummer[14][
        Hypergeometric2F1[a, b, c, z^(-1)]]

Hypergeometric2F1[b + 1 - c, b, b + 1 - a, 
        z^(-1)] == Kummer[14][
        Hypergeometric2F1[b + 1 - c, b, b + 1 - a, 
          z^(-1)]]

Hypergeometric2F1[a, b, c, z^(-1)] == Kummer[15][
        Hypergeometric2F1[a, b, c, z^(-1)]]

Hypergeometric2F1[b + 1 - c, b, b + 1 - a, 
        z^(-1)] == Kummer[15][
        Hypergeometric2F1[b + 1 - c, b, b + 1 - a, 
          z^(-1)]]

Hypergeometric2F1[a, b, c, z^(-1)] == Kummer[16][
        Hypergeometric2F1[a, b, c, z^(-1)]]

Hypergeometric2F1[b + 1 - c, b, b + 1 - a, 
        z^(-1)] == Kummer[16][
        Hypergeometric2F1[b + 1 - c, b, b + 1 - a, 
          z^(-1)]]

Hypergeometric2F1[a + 1 - c, b + 1 - c, 2 - c, z] == Kummer[18][
        Hypergeometric2F1[a + 1 - c, b + 1 - c, 2 - c, z]]

Hypergeometric2F1[a, b, c, z] == Kummer[18][
        Hypergeometric2F1[a, b, c, z]]

Hypergeometric2F1[a + 1 - c, b + 1 - c, 2 - c, z] == Kummer[19][
        Hypergeometric2F1[a + 1 - c, b + 1 - c, 2 - c, z]]

Hypergeometric2F1[a, b, c, z] == Kummer[19][
        Hypergeometric2F1[a, b, c, z]]

Hypergeometric2F1[a + 1 - c, b + 1 - c, 2 - c, z] == Kummer[20][
        Hypergeometric2F1[a + 1 - c, b + 1 - c, 2 - c, z]]

Hypergeometric2F1[a, b, c, z] == Kummer[20][
        Hypergeometric2F1[a, b, c, z]]

Hypergeometric2F1[c - a, c - b, c + 1 - a - b, 1 - z] == Kummer[22][
        Hypergeometric2F1[c - a, c - b, c + 1 - a - b, 1 - z]]

Hypergeometric2F1[a, b, c, 1 - z] == Kummer[22][
        Hypergeometric2F1[a, b, c, 1 - z]]

Hypergeometric2F1[c - a, c - b, c + 1 - a - b, 1 - z] == Kummer[23][
        Hypergeometric2F1[c - a, c - b, c + 1 - a - b, 1 - z]]

Hypergeometric2F1[a, b, c, 1 - z] == Kummer[23][
        Hypergeometric2F1[a, b, c, 1 - z]]

Hypergeometric2F1[c - a, c - b, c + 1 - a - b, 1 - z] == Kummer[24][
        Hypergeometric2F1[c - a, c - b, c + 1 - a - b, 1 - z]]

Hypergeometric2F1[a, b, c, 1 - z] == Kummer[24][
        Hypergeometric2F1[a, b, c, 1 - z]]

Hypergeometric2F1[a, b, c, z] == Kummer[94][
        Hypergeometric2F1[a, b, c, z]]

Hypergeometric2F1[a, b, c, z] == Kummer[95][
        Hypergeometric2F1[a, b, c, z]]

Hypergeometric2F1[a, b, c, z] == Kummer[96][
        Hypergeometric2F1[a, b, c, z]]