Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.al1t)

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=7/2, a₂>=7/2

For fixed z and a₁=7/2, a₂=4, b₁>=-11/2

For fixed z and a₁=7/2, a₂=4, b₁=-11/2

http://functions.wolfram.com/07.25.03.al1t.01

Input Form

HypergeometricPFQ[{7/2, 4}, {-(11/2), -(9/2)}, -z] == (1/442047375) (442047375 - 250047000 z + 178605000 z^2 - 224532000 z^3 + 681080400 z^4 - 10897286400 z^5 - 555761606400 z^6 + 6455940019200 z^7 - 14713401427200 z^8 + 13372337018880 z^9 - 6146755799040 z^10 + 1602444533760 z^11 - 251520675840 z^12 + 24407900160 z^13 - 1462714368 z^14 + 52303872 z^15 - 1015808 z^16 + 8192 z^17) - (1/442047375) ((1024 Sqrt[Pi] (-1758153600 z^(13/2) + 10548921600 z^(15/2) - 19098374400 z^(17/2) + 15500419200 z^(19/2) - 6686517600 z^(21/2) + 1677352320 z^(23/2) - 256888800 z^(25/2) + 24525720 z^(27/2) - 1453485 z^(29/2) + 51570 z^(31/2) - 996 z^(33/2) + 8 z^(35/2)) 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]