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

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=5, a₂>=5

For fixed z and a₁=5, a₂=11/2, b₁>=-11/2

For fixed z and a₁=5, a₂=11/2, b₁=-11/2

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

Input Form

HypergeometricPFQ[{5, 11/2}, {-(11/2), -(3/2)}, z] == (1/88409475) (88409475 + 294698250 z + 2554051500 z^2 - 25540515000 z^3 + 115783668000 z^4 - 527973526080 z^5 + 5279735260800 z^6 + 20745040377600 z^7 + 23885805968640 z^8 + 13065742609920 z^9 + 4005579561984 z^10 + 745489140480 z^11 + 87689629440 z^12 + 6613627776 z^13 + 316902528 z^14 + 9268992 z^15 + 150016 z^16 + 1024 z^17) + (1/88409475) (64 E^z Sqrt[Pi] (169222284000 z^(13/2) + 453515721120 z^(15/2) + 453980252880 z^(17/2) + 230949124560 z^(19/2) + 67835420730 z^(21/2) + 12287243430 z^(23/2) + 1419514173 z^(25/2) + 105744177 z^(27/2) + 5022864 z^(29/2) + 145992 z^(31/2) + 2352 z^(33/2) + 16 z^(35/2)) Erf[Sqrt[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]