Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.0603)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁},{b₁,b₂},z]

Specific values

For integer and half-integer parameters and fixed z

For fixed z and a₁=-11/2, b_1`>=-11/2

For fixed z and a₁=-11/2, b₁=3

http://functions.wolfram.com/07.22.03.0603.01

Input Form

HypergeometricPFQ[{-(11/2)}, {3, 7/2}, z] == (1/(5579410636800 z^2)) (4 (2 z (86225433525 + 1057180855500 z - 1329917263920 z^2 + 304902855360 z^3 - 21447624960 z^4 + 554861568 z^5 - 5410816 z^6 + 16384 z^7) BesselI[0, 2 Sqrt[z]] - Sqrt[z] (151379942175 + 585192138300 z - 1193977365840 z^2 + 294640862400 z^3 - 21174854400 z^4 + 552170496 z^5 - 5402624 z^6 + 16384 z^7) BesselI[1, 2 Sqrt[z]]) - Pi (63212774625 + 674269596000 z + 3146591448000 z^2 - 5034546316800 z^3 + 1198701504000 z^4 - 85240995840 z^5 + 2214051840 z^6 - 21626880 z^7 + 65536 z^8) BesselI[1, 2 Sqrt[z]] StruveL[0, 2 Sqrt[z]] + Pi (63212774625 + 674269596000 z + 3146591448000 z^2 - 5034546316800 z^3 + 1198701504000 z^4 - 85240995840 z^5 + 2214051840 z^6 - 21626880 z^7 + 65536 z^8) BesselI[0, 2 Sqrt[z]] StruveL[1, 2 Sqrt[z]])

Standard Form

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MathML Form

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z </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 3146591448000 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 674269596000 </cn> <ci> z </ci> </apply> <cn type='integer'> 63212774625 </cn> </apply> <apply> <ci> BesselI </ci> <cn type='integer'> 0 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <ci> StruveL </ci> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

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,a₂},{b₁},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂},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]