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

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.annd.01

Input Form

HypergeometricPFQ[{11/2, 11/2}, {-(11/2), 1}, z] == (1/9282994875) (E^(z/2) (9282994875 - 55697969250 z + 142012407600 z^2 - 262677945600 z^3 + 471612456000 z^4 - 1085834030400 z^5 + 6089623545600 z^6 + 28127900021760 z^7 + 32173292067840 z^8 + 16836187737600 z^9 + 4805599518720 z^10 + 809174016000 z^11 + 83169828864 z^12 + 5232500736 z^13 + 195133440 z^14 + 3932160 z^15 + 32768 z^16) BesselI[0, z/2]) + (1/9282994875) (2 E^(z/2) (7873801425 z - 28676818800 z^2 + 57977564400 z^3 - 100344711600 z^4 + 192040178400 z^5 - 549838134720 z^6 + 5714485096320 z^7 + 10326208717440 z^8 + 6515611280640 z^9 + 2053458570240 z^10 + 366648809472 z^11 + 39109244928 z^12 + 2521583616 z^13 + 95625216 z^14 + 1949696 z^15 + 16384 z^16) 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]