Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.am9v)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]

Specific values

For integer and half-integer parameters and fixed z

For fixed z and a₁=4, a₂>=4

For fixed z and a₁=4, a₂=11/2, b₁>=-11/2

For fixed z and a₁=4, a₂=11/2, b₁=-11/2

http://functions.wolfram.com/07.25.03.am9v.01

Input Form

HypergeometricPFQ[{4, 11/2}, {-(11/2), -(7/2)}, -z] == (1/3094331625) (3094331625 - 3536379000 z + 5108103000 z^2 - 14594580000 z^3 + 173675502000 z^4 + 3519823507200 z^5 + 73916293651200 z^6 - 575394444979200 z^7 + 1094407248211200 z^8 - 911989986969600 z^9 + 407449007032320 z^10 - 107948035399680 z^11 + 17928200908800 z^12 - 1920816414720 z^13 + 133831557120 z^14 - 5985570816 z^15 + 164696064 z^16 - 2523136 z^17 + 16384 z^18) - (1/3094331625) ((2048 Sqrt[Pi] (96698448000 z^(13/2) - 444812860800 z^(15/2) + 697366454400 z^(17/2) - 526163299200 z^(19/2) + 221852584800 z^(21/2) - 56686845600 z^(23/2) + 9193587480 z^(25/2) - 969206040 z^(27/2) + 66770055 z^(29/2) - 2962245 z^(31/2) + 81030 z^(33/2) - 1236 z^(35/2) + 8 z^(37/2)) Erfi[Sqrt[z]])/E^z)

Standard Form

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MathML Form

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Rule Form

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Date Added to functions.wolfram.com (modification date)

2007-05-02

HypergeometricPFQ[{},{},z]
HypergeometricPFQ[{},{b},z]
HypergeometricPFQ[{a},{},z]
HypergeometricPFQ[{a},{b},z]
HypergeometricPFQ[{a₁},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅},{b₁,b₂,b₃,b₄},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅,a₆},{b₁,b₂,b₃,b₄,b₅},z]
HypergeometricPFQ[{a₁,...,a_p},{b₁,...,b_q},z]