Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.abxz)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁},{b₁,b₂},z]

Specific values

For rational parameters with larger denominators and fixed z

For fixed z and a₁=3/4, b_1`>=-11/2

For fixed z and a₁=3/4, b_1`=-11/2

http://functions.wolfram.com/07.22.03.abxz.01

Input Form

HypergeometricPFQ[{3/4}, {-(11/2), 23/4}, z] == (1/(824633720832 z^(19/4))) ((19 (4 z^(1/4) (-8754746870244375 - 11672995826992500 Sqrt[z] - 8427333572658000 z - 4121475878520000 z^(3/2) - 1453579288761600 z^2 - 378737322163200 z^(5/2) - 73378088448000 z^3 - 10453051392000 z^(7/2) - 1056964608000 z^4 - 68182605824 z^(9/2) - 2147483648 z^5 + E^(4 Sqrt[z]) (8754746870244375 - 11672995826992500 Sqrt[z] + 8427333572658000 z - 4121475878520000 z^(3/2) + 1453579288761600 z^2 - 378737322163200 z^(5/2) + 73378088448000 z^3 - 10453051392000 z^(7/2) + 1056964608000 z^4 - 68182605824 z^(9/2) + 2147483648 z^5)) + 1740375 E^(2 Sqrt[z]) Sqrt[2 Pi] (5030379585 - 523486656 z + 30868992 z^2 - 1425408 z^3 + 65536 z^4) Erf[Sqrt[2] z^(1/4)] - 1740375 E^(2 Sqrt[z]) Sqrt[2 Pi] (5030379585 - 523486656 z + 30868992 z^2 - 1425408 z^3 + 65536 z^4) Erfi[Sqrt[2] z^(1/4)]))/E^(2 Sqrt[z]))

Standard Form

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MathML Form

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type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 4 </cn> </apply> </apply> </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]