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

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=-9/2

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

Input Form

HypergeometricPFQ[{5, 11/2}, {-(9/2), -(1/2)}, -z] == (1/2679075) (2679075 - 32744250 z - 364864500 z^2 - 1702701000 z^3 - 7718911200 z^4 - 75424789440 z^5 + 281890627200 z^6 - 303574521600 z^7 + 152607732480 z^8 - 42157601280 z^9 + 6904204608 z^10 - 693020160 z^11 + 42728160 z^12 - 1566272 z^13 + 31104 z^14 - 256 z^15) + (1/2679075) ((16 Sqrt[Pi] (9523332000 z^(11/2) - 24321124800 z^(13/2) + 22812042960 z^(15/2) - 10683368640 z^(17/2) + 2831875830 z^(19/2) - 451948140 z^(21/2) + 44602425 z^(23/2) - 2718504 z^(25/2) + 98856 z^(27/2) - 1952 z^(29/2) + 16 z^(31/2)) 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]