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

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=11/2, a₂>=11/2

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

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

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

Input Form

HypergeometricPFQ[{11/2, 11/2}, {-(11/2), 4}, z] == (1/(3094331625 z)) (4 E^(z/2) (310134825 + 732535650 z - 1365903000 z^2 + 1388016000 z^3 - 1247853600 z^4 + 1240868160 z^5 - 1727671680 z^6 + 6206284800 z^7 + 18807655680 z^8 + 12341260800 z^9 + 3426914304 z^10 + 474636288 z^11 + 34099200 z^12 + 1204224 z^13 + 16384 z^14) BesselI[0, z/2]) + (1/(3094331625 z^2)) (4 E^(z/2) (-1240539300 + 164189025 z - 377026650 z^2 + 768511800 z^3 - 816480000 z^4 + 723310560 z^5 - 665340480 z^6 + 761892480 z^7 - 1420830720 z^8 + 10420819200 z^9 + 9533044224 z^10 + 2999943168 z^11 + 442294272 z^12 + 32919552 z^13 + 1187840 z^14 + 16384 z^15) BesselI[1, z/2])

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]