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

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.anci.01

Input Form

HypergeometricPFQ[{5, 11/2}, {-(9/2), -(9/2)}, z] == (1/2531725875) (2531725875 + 3438146250 z + 5472967500 z^2 + 15324309000 z^3 + 115783668000 z^4 + 7919602891200 z^5 + 437349498768000 z^6 + 2412180878688000 z^7 + 4473906656083200 z^8 + 3928236402931200 z^9 + 1916785725281280 z^10 + 568396294502400 z^11 + 108027305164800 z^12 + 13570568355840 z^13 + 1142847912960 z^14 + 64444514304 z^15 + 2386849280 z^16 + 55403520 z^17 + 727040 z^18 + 4096 z^19) + (1/2531725875) (256 E^z Sqrt[Pi] (228559968000 z^(11/2) + 3832774848000 z^(13/2) + 14735085321600 z^(15/2) + 22994718566400 z^(17/2) + 18333694612800 z^(19/2) + 8436751344000 z^(21/2) + 2409380316000 z^(23/2) + 446530527360 z^(25/2) + 55127003490 z^(27/2) + 4585713780 z^(29/2) + 256293465 z^(31/2) + 9430440 z^(33/2) + 217832 z^(35/2) + 2848 z^(37/2) + 16 z^(39/2)) 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]